North British Functional Analysis Seminar

Newsletter 10. — April 1997

Welcome to another issue of the NBFAS Newsletter. Once again, contributors have provided a wealth of information and comment: details of a large number of interesting meetings coming up this year and reports of last year’s events, reviews of books just published and news of books expected in 1997, lists of preprints and recent publications, news of visitors and new appointees. My thanks to all who contributed.

If you have any comments or suggestions for the Newsletter, or any items for the next issue, do write to me at: School of Mathematics and Statistics, University of Newcastle upon Tyne, NEWCASTLE UPON TYNE, NE1 7RU. E-mail: Michael.White@newcastle.ac.uk

Michael C. White

PAST, PRESENT AND FUTURE VISITORS

Alan Hopenwasser (University of Alabama) will visit Lancaster in the summer for several months from mid May 1997.

Justin Peters (Iowa State University) will visit Lancaster in October 1997 for several months.

E. Kaniuth (Paderborn) and G. Schlichting (Munich) are continuing the Germano-Aberdonian collaboration. Several visits took place in 1996, and others are expected in 1997, but details have yet to emerge.

E. Kirchberg (Berlin) spent a day in Aberdeen in Sept. 1996, giving two invited talks (and half of an impromptu third) on his recent work.

V.V.Peller It is hoped that V.V.Peller will visit Newcastle for a month in May.

Dr Nets Katz and is visiting Edinburgh as an RA associated with Prof.A.Cabery for two years.

Dr Gianfranco Marletta is visiting Edinburgh until the summer as an RA with Prof.A.Cabery.

Dr S. Perez-Gomez (Madrid) will be visiting Edinburgh from 17 Feb to 24 Mar having recently finished a PhD in harmonic analysis.

Dr Lai Qinsheng (formerly of Leeds and Edinburgh, currently in Canada) will be returning to Leeds in July 1997 to work as research assistant to Jonathan Partington on a threeyear EPSRC funded project entitled Applications of operator theory to the modelling of linear systems.

Various mathematicians – Bill Bade, Rick Loy, George Willis, Marc Thomas – are likely to visit Garth Dales in Leeds in the week or so before the conference in Germany in July. Contact HGD for further details.

FORTHCOMING MEETINGS

CONFERENCE ON BANACH ALGEBRAS

An International Conference on Banach Algebras will be held from 20 July to 3 August 1997 at the Heinrich Fabri-Institute of the University of Tübingen at Blaubeuren, located near Ulm, Germany. It will focus on the general theory of Banach algebras as well as its interplay with other related areas. This the 14th conference in a series: recent meetings were in Newcastle (1995), Winnipeg (1993), and Cambridge (1991). Many of the leading experts are again expected to attend the meeting, which will be partially supported by the Deutsche Forschungsgemeinschaft.

As well as lectures, the conference will include eight workshops dedicated to more specialised areas. The chairmen of these workshops are:

W.G. Bade (Berkeley): Algebraic Structure of Banach Algebras
B. Chevreau (Bordeaux): Dual Banach Algebras and Invariant Subspaces
H.G. Dales (Leeds): Automatic Continuity
J. Eschmeier (Saarbrücken): Local Spectral Theory
J. Esterle (Bordeaux): Banach Algebras and Analytic Functions
N. Gronbæk (Copenhagen): Amenability
A. Ya. Helemskiĭ(Moscow): Banach Homology
G. Willis (Newcastle, Australia): Banach Algebras in Harmonic Analysis

For further details contact the conference organisers, E.Albrecht and M. Mathieu, at ba97@math.uni-sb.de or H.G.Dales at pmt6hgd@leeds.ac.uk.

L.M.S. Workshop on “Limit Algebras” at Ambleside and Lancaster

Stephen Power reports:

“The London Mathematical Society has agreed to fund my proposal for a small workshop on Limit Algebras. This event has a two phase format the first of which is in Ambleside, from 30 June–4 July 1997, and the second at Lancaster University, from 5th July–13 July, roughly......”

“...With “imposed informality” and a low density of formal talks I think the workshop has the potential for generating exciting projects. I anticipate that the main themes of contact will be (i) Limit algebras (n-s-a), invariants and classification, (ii) “Limit algebra Banach algebra” ; ideal theory, representations, radicals, (iii) Dynamics, groupoids, antisymmetry, subshifts, lexicography, .........”

(“imposed informality” means an upper bound of 3 formal talks per day !)

Actually the invariants I’m working on at the moment, when I get time, are homology invariants for limit algebras. So there will be some homology in a limit algebra context.

Special Session at American Mathematical Society

There was a special session on Banach algebras at the American Mathematical Society meeting in San Diego in January. This was organised by John Duncan and Michael Neumann - thanks to them for helping to improve the profile of the subject in the US. There were 20 rather short talks over the three days. (HGD)

PEOPLE IN 1996 AND 1997

T. A. Gillespie (Edinburgh) has been appointed to the Chair of Mathematical Analysis at Edinburgh University.

Prof. N. Young (Lancaster) has been appointed to a Chair in Mathematics at Newcastle University. Nicholas takes up his position on 1 April 1997 and we wish him and his wife, Zina (née Lykova), success and happiness in Newcastle. Analysis at Newcastle has received a double benefit from their arrival.

Alan Forrest will be going to Trondheim to work with Christina Skau from the summer.

Olaf Ermert has returned to Germany after two years as a post-doctoral fellow at Leeds. At present he is an assistant at the University of Saarbrücken.

Nick Dudley Ward has completed 3 years as a post-doctoral research assistant at Leeds and is spending the year 1996-97 at INRIA, the Institut National de Recherche en Informatique et en Automatique, in Sophia-Antipolis, France.

Kati Ogden, who finished her Ph.D. at Leeds recently, has been appointed as a mathematics teacher.

Garth Dales is Vice-Chair for Teaching at Leeds for one year from 1 January 1997.

Sheffield telephone numbers

The University of Sheffield now has a new telephone exchange, with new numbers for everyone. The new numbers were shown (in advance of their applicability) in the September 1996 edition of “Mathematical Who’s Where, UK”, but, for the record, here are the numbers for the functional analysts and a few others.

School of Maths. and Stats. Office  0114-22-23800
School of Maths. and Stats. Office (fax)  0114-22-23759
Pure Mathematics Section Office  0114-22-23760
Dr. J. W. Baker (head of Pure Maths. Section) 0114-22-23713
Dr. P. G. Dixon  0114-22-23775
Dr. K. Mackenzie (postgraduate admissions)  0114-22-23745
Professor J. S. Pym  0114-22-23725

The new system also includes a sophisticated answering machine called “Voicemail”, to which you will find yourself connected if there is no reply from the person dialled.

NEWS ITEMS

A Problem of Bade and Curtis

The following problems was raised by Bade and Curtis back in 1960. Let A be a commutative Banach algebra with radical R. Suppose that R is nilpotent and that the quotient A/R is equal to the algebra C(Ω) of all continuous functions on the character space Ω of A. Does it follow that A has a Wedderburn decomposition, in the sense that there is a closed subalgebra B of A such that A = B ⊕R as a semidirect product? Bade and Curtis proved this in the special case where Ω is totally disconnected. There were many attacks on this over the years. The break-through came in the thesis of Michel Solovej at Leeds in 1993 - he established the result in the case where Ω is the unit interval. Finally, in a paper listed below Ernst Albrecht and Olaf Ermert extended Solovej’s methods to give a lovely proof of the general result. It would be nice if a few more of the classic questions from that era were finally resolved. (HGD)

REPORTS OF MEETINGS IN 1996

WORKSHOP ON OSCILLATORY INTEGRALS AND CURVATURE IN HAR-MONIC ANALYSIS ICMS, 14, INDIA STREET, EDINBURGH, SCOT-LAND, 15-18 NOVEMBER 1996.

The workshop was a great success, attracting participants from Russia, Scotland, Italy, Greece, Spain, England, U.S.A., Australia, Canada, Germany, Pais Vasco and the Republic of Ireland. All in all there were 27 participants, slightly over the optimal number, but nonetheless a very workable quantity. (Unfortunately illness prevented Fernando Soria from attending at the very last moment.)

There were 15 presentations made, the last one of which was a joint Workshop/Edinburgh University Mathematics Colloquium given by Professor Carlos Kenig of the University of Chicago.

The topics addressed by the speakers were all within the area of the workshop – curvaturerelated phenomena in harmonic analysis, including multidirectional phenomena, oscillatory integral operators, singular and maximal Radon transforms and the related areas of partial differential equations – and at the cutting edge of modern research in this area. There was also plenty of time for informal discussions, several of which it is hoped will bear fruit in the near future. In particular, the wine reception followed by a French meal on the Friday night acted as a good way to loosen people’s tongues!

The workshop was attended by many Ph.D. students and young post-docs. The feedback from them has been very positive indeed. They felt the format provided a far better way to involve themselves both in the mathematics and with the people than that of a traditional large scale conference.

The following were the principal participants:

M. Agranovich (Moscow & Heriot-Watt), T. Bailey (Edinburgh), W. Beckner (Austin, Texas), M. Bramanti (Milano), A. Carbery (Edinburgh), J. Duoandikoetxea (Bilbo), A. Etheridge (QMW), T.A. Gillespie (Edinburgh), C. Kenig (Chicago), D. Müller (Kiel), F. Ficci (Torino), A. Sinclair (Edinburgh), J. Wright (UNSW), S. Ziesler (UC Dublin).

It is hoped that this workshop will be the first in an occasional series at Edinburgh.

NBFAS at Sheffield March 1996

NBFAS first meeting at Sheffield took place on 4th March 1996 with Dr Christian Le Merdy (Franche-Comte) as speaker.

Operator algebras structures on commutative and non commutative l^{p} spaces.

The lectures considered which Banach spaces could be viewed as algebras of operators on Hilbert space. This topic attracted the attention of Varopoulos, Davie and others in the late 1960’s and the speaker began with a review of the classical results. Since then, the theory of operator spaces has developed, and the first lecture included a detailed description of the new formalism of matricially normed spaces.

In the second lecture the operator space theory was applied to describe operator algebra structures on the Schatten ideals C_{p} and on row/column spaces of matrices. Two of the most significant results were:

C_{p} is a Q-algebra for 2 ≤ p ≤ 4 and

row ∩ column space is a matricial Q-algebra.

The proof of the second result depends upon an operator algebra version of Khintchine’s inequality, as interpreted in the non-commutative setting by Lust-Piquard and Pisier. The attendance of 16 was relatively low, presumably due to the travel time to Sheffield.

Dr. G. Blower (Secretary)

Report on Meeting at Edinburgh

The 1996 Summer Meeting at Edinburgh was held at George Square on the Late Spring Bank Holiday with Ken Dykema (Odense) and V. Vasyunin (St. Petersburg) as speakers.

Free probability theory and von Neumann algebras related to free groups

Dykema’s first lecture was an introduction to non commutative probability theory. The fundamental notion of freeness was introduced, motivated by Voiculescu’s matrix model. Although this idea arises in statistical mechanics, the speaker’s main concern was with L(F_{n}) the von Neumann algebras generated by the left regular representation of the free group F_{n}. A problem of Kadison asks whether different n ≥ 2 give rise to distinct algebras. The speaker discussed several results relating to the dimension of L(F_{n}) and interpolated groups F_{t}.

The second lecture described recent work of Dykema, Haagerup and Rordam on free entropy. This concept was introduced by Voiculescu to analyse maximal Abelian subalgebras of L(F_{n}). Some of the continuity properties of entropy depend upon deep probabilistic inequalities related to the isoperimetric inequality. This lecture was an attractive introduction to a subject which will develop in importance.

After de Branges’ proof of the Bieberbach conjecture

At the Leeds meeting of 1992, Nikolskii described an operator-theoretic approach to the de Branges’ Theorem on coefficients φ̂(n) of univalent functions φ(z) on 𝔻. Vasyunin, the co-author of this epic work, showed how the Robertson, Milin and Bieberbach conjectures could be viewed as operator inequalities for the composition operator f ↦ f ∘ φ on Dirichlet space {f holomorphic : ∫∫_{𝔻} |f′|^{2} < ∞}. The lecture included as clear discussion of the Lowner equation. This was originally introduced to settle particular cases of the Bieberbach conjecture, but more generally could be viewed as a differential equation satisfied by extremal vectors for an evolution family of composition operators. Beurling’s description of the shift invariant subspaces and the Riemann Hypothesis

The second lecture of Vasyunin began with a striking statement of how the Riemann Hypothesis is implied by a density condition for subspaces of Hilbert space L^{2}((1, ∞), dx/x^{2}). Several other Hilbert space approaches to the Riemann Hypothesis were described, some of which made sense of Mellin transform calculations involving ζ(s) which had previously baffled this reviewer.

Fair weather, good talks and an attendance of over thirty contributed to a successful meeting.

Dr. G. Blower (Secretary)

Report on Meeting at Glasgow

The Autumn meeting of NBFAS was held at Glasgow on 1st/2nd November 1996 with Alfons van Daele (K.U. Leuven) and Robert Deville (Bordeaux) as speakers.

Discrete and compact quantum groups in the operator algebra approach

Van Daele’s lectures were concerned with the generalization of the following classical result. For any locally compact abelian group G the dual group Ĝ of characters is again a locally compact abelian group. The dual of Ĝ is canonically isomorphic to G. If G is compact, then Ĝ is discrete. To generalize this to the setting of compact groups, one uses the notion of a Hopf algebra. In the first lecture it was shown that to obtain a duality theory for discrete groups and the (non-unital) algebra A of finitely supported functions G → C, it is profitable to introduce the notion of a multiplier Hopf algebra. In this theory the comultiplication is a homomorphism A → M(A ⊗ A) to the multiplier algebra of A ⊗ A. Assuming that A has a non-zero left invariant functional one can establish a biduality theorem analogous to Pontyagin’s.

In the second lecture the ∗-algebra case was considered in detail. When a positive invariant functional is present one can form a GNS representation of A and create an analogue of the left regular representation. Both talks were evidently very carefully prepared and were smoothly delivered.

Smooth Variational Principles

The next day’s lectures dealt with a contrasting but equally fashionable topic, namely the differentiability of functions on Banach spaces. This topic originates in the calculus of variations where minimisation problems are used to solve non linear differential equations. Although this can be a rather technical topic, Deville gave an accessible and clear account of some recent results. He began by presenting an elementary example of a differential equation with no classical solution but a continuum of weak solutions. This motivated the introduction of viscosity solutions defined in terms of sub and super-differentials. It was shown that for a Banach space X of type (H1) (admitting a C^{1} smooth bounded Lipschitz bump function) any lower semicontinuous positive u : X → R may be perturbed by a smooth function φ of arbitrarily small supremum norm so that u − φ attains its minimum.

Hamilton Jacobi equations

In the second lecture the speaker considered how to prove uniqueness of solutions of the Hamilton Jacobi equations. To achieve a smooth variational principle with constraints it appears necessary to suppose either that X is finite dimensional or that the functions involved are uniformly continuous. This surprising fact nevertheless leads to a satisfactory answer to the original problem. The combined attendance for the lectures was over 26, with an unusually large number of graduate students. Dismal weather forced cancellation of some intended hill walks, but the mathematics should have been a good compensation.

Dr. G. Blower (Secretary)

Report on the NBFAS Meeting at Leeds.

A meeting of NBFAS was held at Leeds on 3rd March 1997.

An audience of 23, including two from Birmingham, attended the lectures

On a Hilbert space for Dirichlet series by Professor Hakan Hedenmalm of Lund.

The speaker began by reviewing the classical results on the various abscissa of convergence for the Dirichlet series f(s) = ∑_{n} a_{n}n^{−s}. The Hilbert space H considered in the remainder of the talk was the space of f with ∥f∥_{H}^{2} = ∑_{n} |a_{n}|^{2} < ∞. Such functions are analytic and bounded on the half plane ℜs > 1/2 + ε. A function φ is a multiplier of H if φf ∈ H for each f ∈ H; let M be the space of such. It is easily seen that M ⊂ H (φ1 ∈ H) and M ⊂ H^{∞}(ℜs > 1/2) (on considering |(φ^{n}f)(s)|^{1/2} ). In fact M = H ∩ H^{∞}(ℜs > 0).

The proof depends Carlson’s alternate expression for the norm of H;

if f ∈ H^{∞}(ℜs > 0) is a Dirichlet series then f ∈ H and

∫_{−T}^{T} |f(σ + it)|^{2}dt/(2T) → ∑_{n=1}^{∞} |a_{n}|^{2}n^{−2σ} as T → ∞.

In the second lecture the speaker considered the space of multiplicative maps ϕ : N → D ∪ {1}; these may be identified with the sequences ϕ(p) ∈ D with p primes. One can view f ∈ H as a function on the pseudo-characters ϕ by f(ϕ) = ∑_{n} a_{n}ϕ(n) with absolute convergence for (ϕ(n)) ∈ D^{∞} ∩ ℓ_{n}^{2}. This makes f into a function of infinitely many complex variables z_{p} = ϕ(p). He then stated some results concerning generic behaviour of the series f_{χ}(s) = ∑_{n} a_{n}χ(n)n^{−s} with respect to Haar measure on the characters χ. For almost all χ, ζ(s) = ∑_{n} χ(n)n^{−s} has no zeros with ℜs > 1/2.

The Riemann Hypothesis in almost surely valid!

The final application of multipliers concerned Riesz bases. Let φ ∈ L^{2} be odd and 2periodic; set φ_{n}(x) = φ(nx), and let (a_{n}) be the coefficients in the Fourier expansion φ(x) = ∑_{n} a_{n}\sqrt{2} sin 2πnx in L^{2}(0, 1). Then the (φ_{n}) are a Riesz basis of L^{2}(0, 1) if and only if ∑_{n} a_{n}n^{−s} and its reciprocal are in M.

The lectures were delivered in an attractive, leisurely style; the new results may be found in H.H., P. Lindqvist and K. Seip, ‘A Hilbert space of Dirichlet series and systems of dilated functions in L^{2}(0, 1)’, Duke Math. J. 86 (1997), 1-37.

G. Blower, Secretary

Report on a Workshop in Functional Analysis at the Euler International Mathematical Institute, St Petersburg

This was attended by G.V.Wood (Swansea), M.C.White (Newcastle), B.E.Johnson (Newcastle), J.Kyle (Birmingham), H.G.Dales (Leeds), T.A.Gillespie (Edinburgh), J.Brodzki (Exeter), C.H.Chu (Goldsmiths), M.M.Dodson (York).

I was lucky enough to be invited to participate in the British-Russian Workshop in Functional Analysis held at the Euler International Mathematical Institute, St Petersburg, 13–17 October 1996. The institute is in an elegant building close to a river and was once the summer house of an aristocrat. The workshop was a very stimulating and enjoyable experience. There were about 30 participants, from different parts of the former Soviet Union and from England, Scotland and Wales (3 out of the 4 parts of the present UK). It was very nice to see some very keen and able younger mathematicians, including research students, at the meeting.

The scientific programme focussed mainly on two areas, the cohomology of Banach algebras and operator theory. In the former there are prominent schools in both Russia and Britain, and there were several talks bearing witness to continuing activity in the field. In operator theory it was the first opportunity for many of the British participants to meet representatives of the powerful Ukrainian school as well as to meet or renew acquaintance with mathematicians from St. Petersburg, which remains a hotbed of analysis. Twenty-six talks were given, there was a good standard of presentation and I believe participants got a good impression of the nature of current research in the two fields in the countries concerned.

The facilities were excellent. Each participant was allocated an office with a blackboard and a networked PC. The lecture room was a very good size and with a moulded plaster ceiling, upholstered chairs and chandeliers, a pleasure to both sit and lecture in. There are overhead projectors (though these had rather delicate bulbs) and excellent stateof-the-art blackboards (much better than ours at York). There was a pleasant library (though not very well stocked), a room for discussion and refreshments of tea, coffee and biscuits. The Euler Institute is associated with the Steklov Institute and naturally there are links with the other mathematical departments in universities and institutions in the city.

The city of St Petersburg was a tremendous bonus; it must be one of the most beautiful in the world. Access to the city centre was good, by the metro or by tram. The Hermitage is of course one of the great art galleries of the world and needs several days to see properly. As well there is the opera (we were taken to a sumptuous performance of ‘Prince Igor’), the concerts and the city’s magnificent architecture to enjoy.

The atmosphere was altogether most agreeable and we were made to feel very welcome by our organiser Vasily Vasyunin and the Institute staff. Everyone was friendly and helpful, indeed I arrived on a late flight and was met at the airport and taken to the hotel near the Institute. The accommodation was comfortable and reasonably priced. Prior to leaving Britain, regular and helpful emails from Elena Novikova kept us informed of the arrangements for accommodation and the workshop. The inevitable administrative formalities were minimal and the visits to the city, the Hermitage and the opera were well organised. A good deal of the credit for the success of the Workshop must go to the organisers and the efficient and unobtrusive staff. On behalf of the British contingent I would like to thank them all very much and I hope there will be another opportunity to visit the Euler Institute.

Maurice Dodson, York

PREPRINTS

The bracketed letters after a name indicate the relevant member university (e.g. (LE) = Leeds, (LA) = Lancaster). Departmental addresses are listed at the end of the Newsletter. J. Agler and N.J. Young, ‘Which function spaces have the Adamyan-Arov-Krein property?’ Preprint 1997. E. Albrecht and O. Ermert (LE) , ‘Commutative nilpotent extensions of commutative C^{∗} algebras split’, Bull. London Math. Soc., to appear.

R.J. Archbold (A), E. Kaniuth, ‘On the primitive ideal space of a finitely generated nilpotent group’, Math. Forum, to appear. R.J. Archbold (A), E. Kaniuth, ‘Simply connected nilpotent Lie groups with quasi-standard C*-algebras’, Proc. Amer. Math. Soc., to appear. R.J. Archbold (A), E. Kaniuth, G. Schlichting, D.W.B. Somerset (A), ‘Ideal spaces of the Haagerup tensor product of C*-algebras’, Internat. J. Math., to appear. R.J. Archbold (A), J.S. Spielberg, ‘Upper and lower multiplicity for irreducible representations of C^{∗}-algebras’, II, J. Operator Th., to appear. R.J. Archbold (A), D.W.B. Somerset (A), J.S. Spielberg, ‘Upper multiplicity and bounded trace ideals in C^{∗}-algebras’, J. Funct. Anal., to appear N. Asmar, E. Berkson and T.A. Gillespie, ‘Note on norm convergence in the space of weak type multipliers’ W.G. Bade, H.G. Dales (LE), Z.A. Lykova (LA), ‘Algebraic and strong splittings of extensions of Banach algebras’, 107pp. J.W. Baker (Sheff) and M. Filali (Oulu), ‘Minimal ideals in group algebras and their biduals’, Math. Proc. Camb. Phil. Soc. 120 (1996), 475-488. E. Berkson and T.A. Gillespie, ‘The q-variation of functions and spectral integration of Fourier multipliers’ E. Berkson and T.A. Gillespie, ‘Mean boundedness and Littlewood-Paley for separation-preserving operators’ E. Berkson, I.R. Doust and T.A. Gillespie, ‘Properties of AC operators’ E Berkson and T.A. Gillespie, ‘Multipliers of weighted L^{p} spaces, transference, and the qvariation of functions’ T.J.Blackmore (PhD student Sheffield), ‘Weak amenability of discrete semigroup algebras’, to appear in Semigroup Forum T.J.Blackmore (PhD student Sheffield), ‘Derivations from totally ordered semigroup algebras into their biduals’, to appear in Canad. Math. Bull. G. Blower, ‘Quadratic integrals for operator valued functions’ Submitted to Bulletin des Sciences, June 1996. G. Blower, ‘Quadratic integrals and the Williams operator’, Submitted to Studia Mathematica, April 1996. G. Blower, ‘Bilinear forms on vector Hardy spaces’, Glasgow Mathematical Journal. To appear. G. Blower, ‘Functional calculus and absolutely summing operators’, submitted to Proceedings of the Edinburgh Mathematical Society, November 1996. C. Bonnet and J.R. Partington (LE), ‘Bézout factors and L^{1}-optimal controllers for delay systems using a two-parameter compensator scheme.’ A. Carbery, F. Ricci and J. Wright, ‘Maximal functions and Hilbert transforms associated with polynomials’ A. Carbery and F. Soria’, ‘Pointwise Fourier inversion and localization in R^{n}’ H.G. Dales (LE), F. Ghahramani and N. Grønbæk, ‘Derivations into iterated duals of Banach algebras.’ H.G. Dales (LE) and R.J. Loy, ‘Uniqueness of the norm topology for Banach algebras with finite-dimensional radical’, Proc. London Math. Soc, (3), 74, to appear. H.G. Dales (LE) and V. Runde , ‘Discontinuous homomorphisms from non-commutative Banach algebras’, Bull. London Math Soc., to appear. O. Ermert (LE), ‘Hochschild cohomology groups of certain algebras of analytic functions with coefficients in one-dimensional bimodules.’ O. Ermert (LE), ‘A lower bound on the homological bidimension of a non-unital C^{∗}-algebra.’ J. Eschmeier (LE), ‘Invariant subspaces for spherical contractions.’ T.A. Gillespie, ‘Boundedness criteria for Boolean algebras of projections’ J.J. Green (Sheffield postgraduate), ‘Banach algebras of topologically bounded index’, to appear in Bull. Austral. Math. Soc.. G.J.O. Jameson, ‘Khinchin’s inequality for operators’, Glasgow Math. J., to appear. G.J.O. Jameson, ‘2-convexity and 2-concavity in Schatten ideals’, Math. Proc. Cambridge Phil. Soc., to appear Oct. 1996. N. Katz, Three preprints on harmonic analysis; may be copied from http://www.maths.ed.ac.uk/ñets/ A. Kumar and A.M. Sinclair, ‘Equivalence of norms on operator space tensor products of C^{∗} algebras’ D. Lamb (LE), ‘Beurling and Lipschitz algebras.’ D. Lamb (LE), ‘The second dual of certain Beurling algebras.’ E.C. Lance (LE), ‘Finitely-presented C^{∗}-algebras.’ N.J. Laustsen (LE), ‘K-theory for algebras of operators on Banach spaces.’ Z.A. Lykova (LA), ‘Examples of Banach algebras over commutative Banach algebras with given homological dimension’, 15pp. P.M. Mäkilä and J.R. Partington (LE), ‘Lethargy Results in LTI system modelling.’ P.M. Mäkilä, J.R. Partington (LE), and T. Norlander ‘Bounded power signal spaces for robust control and modelling.’ A. Paolucci (LE) and I. Tsohantjis, ‘Hopf-Type deformed oscillators, their quantum double and a q-deformed Calogero-Vasiliev Algebra.’ J.R. Partington (LE) and B. Ünalmış (LE), ‘On the representation of shift-invariant operators by transfer functions.’ S.C. Power and C. Laurie, ‘On the C^{∗}-envelope of approximately finite-dimensional operator algebras’, Math. Skandinavika, to appear. S.C. Power and A. Katavolos, ‘The Fourier Binest Algebra’, Math. Proc. Camb. Phil. Soc., to appear. S.C. Power and A.P.Donsig, ‘The failure of approximate inner conjugacy for standard diagonals in regular limit algebras’, preprint, Bulletin Canadian Math. Soc., to appear. S.C. Power and D. Heffernan, ‘Limits of sums of digraph algebras with reduced digraphs having two vertices’, International J. Math., to appear. S.C. Power, ‘Completely contractive representations of some doubly generated antisymmetric operator algebras’, Proc. Amer. Math. Soc., to appear. S.C. Power, ‘Partly self-adjoint limit algebras’, to appear in the Proceedings of a NATO ASI, Samos, Greece 1996. F. Sady (LE), ‘Algebras of operators as topological algebras.’ Yu.V.Selivanov, ‘Global dimension theorem for weighted convolution algebras’, F. Ghahramani and Yu.V. Selivanov, Proc. of Edinburgh Math. Soc., to appear. A.M. Sinclair and R.R. Smith, ‘Factorization of completely bounded bilinear operators and injectivity’ D.W.B.Somerset (A), ‘The proximinality of the centre of a C^{∗}-algebra’, J. Approx. Th., to appear. D.W.B.Somerset (A), ‘The central Haagerup tensor product of a C^{∗}-algebra’, preprint. D.W.B.Somerset (A), ‘A Dauns-Hofmann theorem for TAF-algebras’, preprint. H. Steiniger (LE), ‘Finite-dimensional extensions of the Fourier algebra’ P.N. Tapper (LE), ‘Free contractive C^{∗}-algebras and C^{∗}-ideals. ’ P.N. Tapper (LE), ‘C^{∗}-ideals generated by polynomials.’

RECENT PUBLICATIONS — PAPERS.

J. Agler and N.J. Young, ‘Functions which are almost multipliers of Hilbert function spaces’, 27 pages. MSRI Preprint 1996-039 (accessible at http://www.msri.org/MSRIpreprints/online/1996-039.html) L. Baratchart, J. Leblond and J.R. Partington (LE), ‘Hardy approximation to L^{∞} functions on subsets of the circle’, Constructive Approximation 12 (1996), 423–435. S.J. Bhatt and H.V. Dedania (LE), ‘Uniqueness of the uniform norm and adjoining identity in Banach algebras’, Proc. Indian Acad. Sci. – Math. Sci. 105 (1995), 405–409. G. Blower, ‘Stationary processes for Translation Operators’ Proc. London Math. Soc.(3) 72 (1996) 697-720. G. Blower, ‘Multipliers for semigroups’ Proc. Edinburgh Math. Soc. 39 (1996), 241-252. G. Blower, ‘Complete polynomial bounds for matrices’ 5 pages Quart. J. Math. Oxford (2) 48 (1997). G. Blower, ‘Quadratic integrals and factorization of linear operators’ J. London Math. Soc.,(2) 18 pages. To appear. H.G. Dales (LE), Review of “Banach algebras and the general theory of *-algebras” (by T.W. Palmer), Bull. London Math. Soc. 28 (1996) 656–659. P.G. Dixon (Sheffield), ‘Topologically irreducible representations and radicals in Banach algebras’, Proc. London Math. Soc. (3), 74 (1997), 174–200. N.F. Dudley Ward (LE) and J.R. Partington (LE), ‘Rational wavelet decompositions of transfer functions in Hardy-Sobolev classes’, Math. Control Signals Systems 8 (1995), 257–278. N.F. Dudley Ward (LE) and J.R. Partington (LE), ‘Robust identification in the disc algebra using rational wavelets and orthonormal basis functions’, Int. J. Control 64 (1996), 409–423. O. Ermert (LE), ‘Continuity of homomorphisms from AF-C^{∗}-algebras and other inductive limit C^{∗}-algebras’, J. London Math. Soc. 54 (1996), 369–386. J. Eschmeier (LE), K.B. Laursen and M.M. Neumann, ‘Multipliers with natural local spectra on commutative Banach algebras’, J. Functional Anal. 138 (1996), 273–294. Q.S. Lai (LE), ‘A note on the weighted norm inequality for the one-sided maximal operator’, Proc. Amer. Math. Soc. 124 (1996), 527–537. Z.A. Lykova (LA), ‘Excision in Banach simplicial and cyclic cohomology groups’, to appear in Proceedings of the Edinburgh Math. Soc.; MSRI Preprint 1996-046, Math. Sciences Research Institute, Berkeley, U.S.A., 15pp. Z.A. Lykova (LA), ‘Relative cohomology of Banach algebras’, MSRI Preprint 1995-091, Math. Sciences Research Institute, Berkeley, U.S.A., 24pp. C.P. Ogden (LE), ‘Homomorphisms from B(C(ω_{η}))’, J. London Math. Soc. 54 (1996), 346– 358. J.R. Partington (LE), ‘Recovery of functions by interpolation and sampling’, J. Math. Anal. Appl. 198 (1996), 301–309. J.R. Partington (LE) and P.M. Mäkilä, ‘Modelling of linear fading-memory systems’, IEEE Trans. Auto. Control 41 (1996), 899–903. V.V. Peller and N.J. Young, ‘Superoptimal approximation by meromorphic functions’, Math. Proc. Camb. Phil. Soc. 119(1996) 497-511. V.V. Peller and N.J. Young, ‘Continuity properties of best analytic approximation’, MSRI preprint 1995. To appear in J. für die Reine und Angewandte Mathematik, February 1997. S.C. Power, ‘Lexicographic semigroupoids’, J. Ergodic Theory and Dynamical Systems,16 (1996), 365-377.

S.C. Power, ‘Homology for Operator Algebras II : Stable homology for non-self- adjoint algebras’, J. Functional Anal., 135 (1996), 233-269. S.C. Power, ‘On the Banach space isomorphism type of AF C*-algebras and their triangular subalgebras’, Israel J. Math., 94 (1996), 93-109 Yu.V.Selivanov, ‘Weak homological bidimension and its values in the class of biflat Banach algebras’, Extracta Math. 11, n. 1 (1996), 1-18. Yu.V.Selivanov, ‘Frechet algebras of global dimension zero’, in “Algebra. Proc. of the IIIrd Int. Conf. on Algebra held in Krasnoyarsk, Russia, Aug. 23-28, 1993”, de Gruyter, 1996, 225-236. N.J. Young, ‘Some function-theoretic issues in feedback stabilisation’, to appear in the Proceedings of the 1995 Semester on Holomorphic Spaces, MSRI, Berkeley.

M.SC. AND PH.D. THESES

A.J. Oliver “Matricial Structures and Inequalities for the Schatten p-ideals”, PhD thesis awarded 1996, supervisor T.A. Gillespie.

J.J. Green (Sheffield) “Uniform convergence to the spectral radius and some related properties in Banach algebras” (October 1996)

Tim J. Blackmore (PhD student Sheffield, now working at Centre for Communications Research, University of Bristol), “On the weak amenability of certain Banach algebras”

David Lamb (LE) “Beurling and Lipschitz algebras” (Ph.D.)

Paul Tapper (LE) “Embedding ∗-algebras into C^{∗}-algebras” (Ph.D.)

Rasoul Pourabbas (NCL) “The Cohomology of some Banach Algebras” (Ph.D.)

Nik Nik Long (LE) “Wavelets and the pyramid algorithm” (M.Sc.)

FORTHCOMING BOOKS

J. Eschmeier (LE) and M. Putinar, ‘Spectral decompositions and analytic sheaves’, London Math Soc Monographs 10, Clarendon Press, Oxford, 1996.

H.G. Dales (LE) and W.H. Woodin, ‘Super-real fields Totally ordered fields with additional structure’, London Math Soc Monographs 14, Clarendon Press, Oxford, 1996.

Jonathan R. Partington(LE) ‘Interpolation, Identification and Sampling’, London Mathematical Society Monographs, Oxford University Press. Expected publication date, June 1997.

This book is concerned with applications of functional analysis and complex analysis to interpolation in spaces of analytic functions. The problems considered are those of recovery, producing approximations to functions from measured values. These values may in turn be corrupted by small errors and we wish to be able to produce a good approximation using this partial and inaccurate information. The practical applications include systems identification, and also signal processing and sampling. Contents: Function spaces and operators, Interpolation and recovery, Worst-case identification of functions, Approximation and interpolation, Hilbert space methods, Convolution operators, Sampling, Applications.

MEMBER UNIVERSITIES, COMMITTEE MEMBERS 1996–7

\underline{Aberdeen} (1 unit) Dr. D. W. B. Somerset, Department of Mathematics, The Edward Wright Building, Dunbar Street, ABERDEEN, AB9 2TY. e-mail: ds@maths.abdn.ac.uk Fax: 01224 272607 Tel: 01224 272755

\underline{Cambridge} (1 unit) Dr. T. W. Körner, Department of Pure Mathematics, 16 Mill Lane, CAMBRIDGE, CB2 1SB. e-mail: t.w.korner@dpmms.cambridge.ac.uk Tel: 01223 337999/332500

\underline{Edinburgh} (4 units) Prof.Allan Sinclair, Department of Mathematics and Statistics, James Clerk Maxwell Building, University of Edinburgh, The King’s Buildings, Mayfield Road, EDINBURGH, EH9 3JZ. e-mail: allan@maths.ed.ac.uk Fax: 0131 650 6553 Tel: 0131 650 5083

\underline{Glasgow} (3 units) Dr. A. S. Wassermann, Department of Mathematics, University of Glasgow, University Gardens, GLASGOW, G12 8QW. e-mail: GAMX02@cms.glasgow.ac.uk Tel: 0141 339 8855

\underline{Heriot-Watt} (1 unit) Dr. M. Youngson, Department of Mathematics, Heriot-Watt University, Riccarton, EDINBURGH, EH14 4AS. e-mail: martin@ma.hw.ac.uk Fax: 0131 451 3249 Tel: 0131 451 3241

\underline{Lancaster} (3 units) Department of Mathematics, University of Lancaster, Bailrigg, LAN-CASTER, LAl 4YL. Fax 01524 841710 Tel: 01524 65201 Prof. N. J. Young (ex Local representative), e-mail: N.J.Young@lancaster.ac.uk Dr. G. Blower (Secretary), e-mail: G.Blower@lancaster.ac.uk Tel: 01524 593962 Prof. S. C. Power (Treasurer), e-mail: S.C.Power@central1.lancaster.ac.uk Tel: 01524 593958

\underline{Leeds} (3 units) Dr. J. R. Partington, School of Mathematics, University of Leeds, LEEDS, LS2 9JT. e-mail J.R.Partington@leeds.ac.uk URL: http://amsta.leeds.ac.uk/Pure/staff/partington/partington.html Fax: 0113 233 5145 Tel: 0113 233 5123

\underline{Manchester} (3 units) Prof. R. J. Plymen, Dept. of Mathematics, The University of Manchester, MANCHESTER, M13 9PL. e-mail: ROGER@ma.man.ac.uk Tel: 0161 275 2000

\underline{Newcastle} (3 units) Dr. M. C. White, School of Mathematics, Merz Court, The University of Newcastle-upon-Tyne, NEWCASTLE-UPON-TYNE, NE1 7RU. e-mail: Michael.White@newcastle.ac.uk Tel: 0191 222 6000

\underline{Sheffield} (2 units) Dr. P. G. Dixon, Pure Mathematics Section, School of Mathematics and Statistics, University of Sheffield, SHEFFIELD, S3 7RH. e-mail: P.Dixon@sheffield.ac.uk URL: http://www.shef.ac.uk/ ms/staff/dixon/ Tel: 0114 22 23775