North British Functional Analysis Seminar

Newsletter 9. — March 1996

Welcome to another issue of the NBFAS Newsletter. Once again, contributors have provided a wealth of information and comment: reports of last year’s events, reviews of books just published and news of books expected in 1996, lists of preprints and recent publications, news of visitors and new appointees. My thanks to all who contributed.

Unfortunately there was no information from Lancaster in last year’s Newsletter. They make up for it this year with a bumper crop of papers and news.

If you have any comments or suggestions for the Newsletter, or any items for the next issue, do write to me at: Department 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

LEEDS-SAARBRÜCKEN LINK

Groups in functional analysis at Leeds and Saarbrücken have formed a link, funded by the British Council and DAAD. H.G. Dales and J.R. Partington will visit Saarbrücken in January and May 1996, respectively; Volker Runde will visit Leeds for the month of March 1996, and Sandra Pott will visit in February 1996.

Prof. Tim Feeman (Villanova University in Pennsylvania) visited Lancaster from January to July in 1995.

Allan Hopenwasser intends to spend several months leave at Lancaster in 1997. Allan’s current research is almost entirely devoted to the structure and classification of non-self-adjoint limit algebras.

E. Kaniuth (Paderborn) visited Aberdeen twice last term (Oct., Dec.).

A T Lau (Alberta) Visited the University of Sheffield 1-17 Dec 95 (jointly with JWB). It is hoped that he will be over again in the next six months.

Prof. C. LeMerdy (Bogazici, Istanbul) Visited the University of Sheffield 3–6 March 1996 (around his NBFAS talk on 4 March).

Dr. Florin Pop (Dartmouth College, New Hampshire) will be visiting Lancaster for a year from August 1996 as a Leverhuome Visiting Fellow. Florin’s research concerns operator algebras and cohomology.

Prof. M. Ptak (Krakow) visited Leeds for the whole month of February 1996. He is interested in invariant-subspace results and reflexivity problems for operator algebras. His visit was funded by the TEMPUS programme.

Sandra Pott (Universität des Saarlandes, Saarbrücken) visited Leeds for 2-3 weeks in February 1996. She is working on problems in multivariable operator theory. This is one of a series of visits funded by a German-UK ARC grant.

Dr H. Steiniger (Munster/Paderborn) will be visiting H.G. Dales for one year from July 1996.

Ali Ulger (Bogazici, Istanbul) Visited the University of Sheffield 10-16 July 95.

Professor Zongyao Wang (East China University of Science and Technology, Shanghai) will be visiting Lancaster from February to July 1996. Zongyao, who is a past student of Herrero, is active in research on the approximation of Hilbert space operators and the closures of similarity orbits.

Nicholas Young and Zina Lykova spent the calander year 1995 on sabbatical leave in North America.

PEOPLE IN 1995 AND 1996

Research Assistant

Dr Anna Paolucci will be coming to Leeds to work with Chris Lance on a three-year research grant from EPSRC, starting 1 Febuary 1996. She did her doctoral work with Palle Jorgensen (Iowa) on C^{∗}-algebraic quantum group theory, and will be working on a project to extend the Doplicher-Roberts duality theory for compact groups to the context of compact quantum groups. J.R. Partington

LMS Publications Secretary

Chris Lance has just taken over from Norman Blackburn (Manchester) as Deputy Publications Secretary of the London Math. Soc., the intention being that in a year’s time he should succeed David Brannan (O.U.) as Publications Secretary. With conventional publications (which provide the LMS with its main source of income) increasingly under threat from electronic alternatives, the next few years will be an interesting period for the Publications Secretary. J.R. Partington

Congratulations!!

Jörg Eschmeier has been appointed to a senior professorship (a “C4 chair”) at the University of Saarbrücken, starting next April. We shall be very sorry to lose him and Steliana, after less than two years in Leeds, but we congratulate Jörg very warmly on his appointment and wish both of them all the best for the future. We hope that we shall continue to see them from time to time, since Leeds and Saarbrücken are now linked by a research exchange scheme, as mentioned earlier. J.R. Partington

New appointments at Manchester

The Analysis group at Manchester has been greatly strengthened by the arrival of Richard Sharp as Lecturer, and Mark Pollicott as Fielden Professor. They have already started to organize a fortnightly seminar series in Ergodic Theory and Dynamical Systems. These seminars take place on Thursdays at 4 p.m. R.J. Plymen

REPORTS OF MEETINGS IN 1995

Banach algebra conference in Newcastle, England 17-28 July 1995

The 12th meeting in a sequence of conferences on Banach algebras that goes back to the inaugural meeting in UCLA in 1974 (for a list of the earlier meetings, see below) was held in Newcastle, organized by Barry Johnson and Michael White.

Two or three years ago there was a a feeling that the sequence of these meetings was drawing to a quiet end; we are all getting older, and there is a severe shortage of money from funding bodies to support such meetings and of younger colleagues to carry the torch forward. Happily, Barry and Michael expressed a willingness to organise this meeting in Newcastle, and carried the burden with skill and enthusiasm. On this occassion, they tied in the main meeting with a subsidiary Workshop on Completely Bounded Operators. The outcome was that more people than ever before attended our meeting - indeed, so large was the crowd that we almost collapsed under a wave of talks. Fortunately many of the talks were of very high quality - it was especially valuable to hear lucid surveys of related topics by leading exponents - and the informal and social side were as enjoyable as usual.

We are very grateful to Barry and Michael for their labours and their very generous hospitality.

So successful was the conference there was no discussion whether or not the sequence should continue: Ernst Albrecht and Martin Mathieu will organise the 13th conference at the Heinrich Fabri Institut of the University of Tubingen. H.G. Dales

NORTH BRITISH FUNCTIONAL ANALYSIS SEMINAR Report on the Summer Meeting 1995

A meeting of the North British Functional Analysis Seminar was held at George Square of the University of Edinburgh on Monday 29th and Tuesday 30th May 1995. The meeting was attended by thirty three mathematicians from several Universities in Scotland and the North of England. The meeting enjoyed the financial support of the London Mathematical Society and the British Council, who contributed to Professor Torrea’s travel and subsistence costs. The scientific programme comprised four one-hour lectures.

Dr J. Brodzki (Durham) lectured on Excision in periodic cyclic cohomology and Supertraces and entire cyclic cohomology of Banach algebras.

In his first lecture the speaker introduced the cyclic and periodic cyclic cohomology of a unital algebra via the algebra of non-commutative differential forms. He presented recent results on excision in periodic cyclic cohomology including the Cuntz-Quillen six term exact sequence.

In the second lecture he discussed in detail the Nistor Compatibility Theorem relating the Cuntz-Quillen boundary map of periodic cyclic cohomology to the analytical index map between K-groups of C^{∗}-algebras associated with pseudo-differential operators on a compact manifold. As an application, the Connes-Moscovici Theorem was deduced. Examples of entire cocyles such as the JLO cocyle arising in Quantum Field Theory were also presented.

Prof. J.L. Torrea (Madrid) lectured on Applications of Vector valued harmonic analysis and ergodic theory and The Hardy-Littlewood maximal operator in Banach lattices. In the first talk various classical results on L_{X}^{p} → L_{X}^{p} boundedness of vectorvalued singular integral operators were presented. It was shown that under suitable smoothness assumptions on the operator-valued kernel, the norms of integral operators between vector-valued Lebesgue spaces could be controlled using the scalar Calderon-Zygmund decomposition. Applications to weights, tent spaces, square functions and maximal operators were presented.

In the second lecture the speaker considered the class of Köthe function spaces X for which the Hardy Littlewood maximal operator is bounded L_{X}^{p} → L_{X}^{p} for 1 < p < ∞. Using the techniques described in the previous lecture, various characterizations and structure theorems of this class of spaces X were established. G. Blower

NORTH BRITISH FUNCTIONAL ANALYSIS SEMINAR Report on the Autumn Meeting 1995

A meeting of the North British Functional Analysis Seminar was held at the Department of Mathematics and Weston Conference Centre of the University of Manchester on Friday 10th and Saturday 11th November 1995. It was attended by about twenty-five mathematicians. Regular attenders were supplemented by Manchester graduate students and operator algebraists from Swansea and Exeter.

Professor Paul F. Baum of Pennsylvania State University lectured on Trees, Buildings, Symmetric Spaces and K-Theory for group C^{∗}-algebras.

In his first lecture he reviewed the definition of the K-theory of the C^{∗}-algebra C_{r}^{∗}(G) generated by the left-regular representation of a locally compact topological group G. He showed how the classical results of topological K-theory could be viewed as precursor to non-commutative topology. He explained why the interpretation of the operator Ktheory of C_{r}^{∗}(G) as the topological K-theory of the support of the Plancherel measure was not adequate to cope with such groups as SL(2, R) where the reduced unitary dual space formed a non-Hausdorff topological space.

In his second lecture he considered the universal space \underline{E}G for proper G-actions. It was shown that when G = SL(2, Z) a version of the universal space \underline{E}G could be realised as a tree in the Poincaré disc. The notion of an abstract elliptic operator was introduced in the context of G-spaces, following ideas developed by Atiyah, Kasparov and others. The speaker then presented the unifying conjecture which claims the index map identifies the operator K-theory of C_{r}^{∗}(G) with the G-space K-theory of \underline{E}G defined in terms of abstract elliptic operators. This conjecture, known in index theory as the Baum-Connes Conjecture, remains open in generality but the speaker reviewed several partial positive results pertaining to Lie groups and some consequences of its validity. He discussed an audience question concerning the functorial properties of the terms involved in the conjecture. The lectures were delivered in a clear, lively style.

The following day the meeting continued at the Weston Conference Centre (UMIST) with a smaller audience.

Professor Mariusz Wodzicki (Berkeley, visiting Paris) lectured on Flatness in Functional Analysis.

In his first talk the speaker reviewed the definition of the Hochschild cohomology of a bimodule over a Banach algebra. He introduced the comparison maps from continuous to algebraic Hochschild cohomology groups and described bar resolutions of Banach modules.

In his second talk the notion of flatness was introduced in the algebraic and functional analytic settings. The speaker recalled results showing that the value of the projective dimension of the field of rational functions in three commuting indeterminates over the complex numbers depends upon the assumption of the continuum hypothesis or its negation. It was also shown that one’s precise choice of set theory axioms becomes involved when one attempts to compute the global homological dimension of B(H) . G. Blower

LMS Invited Lectures 1995

The LMS Invited Lectures 1995 were given by Paul Baum, Distinguished Professor at Penn State University, USA. The talks were entitled “Trees, Buildings, Symmetric Spaces and the K-Theory of C^{∗}- algebras”. This was a superlative set of 10 talks, immaculately prepared in SLITEX. Paul managed to include a significant amount of technical material on the Kasparov groups KK(A, B), as well as providing the audience with a very clear sense of direction. The talks led up to the Baum-Connes conjecture for separable locally compact groups G. This conjecture amounts to a conjectured “answer” for the K- groups of the reduced C^{∗}-algebra of G. The conjecture has three aspects, when the group G is a Lie group, a p-adic group, or a discrete group. R.J. Plymen

Topological algebras.

A meeting was organised by Wieslaw Zelazko and J. Zermanek at the Banach Center in Warsaw 23-27 October 1995; the meeting was attended by H.G. Dales and G.R. Allan. It was a pleasure to meet a large contingent of functional analysts from Athens, led by Professor A. Mallios; in particular we met Dr Maria Fragoulopoulou, quondam M.Sc. student at Newcastle, now Mrs A.Ya. Helemskii. Dr L. Pugach of Bryansk - recovered from his visit to Newcastle - was also accompanied by his new wife. Best wishes to these two couples. The Banach Center is under some threat because it is conceivable that, under a new Polish law, the descendants of a former owner of the Center might be able to claim some right to the building. J.R. Partington

Truth in Mathematics.

The meeting in Mussomeli advertised in the last Newsletter took place in September 1995 - we survived chaos of aeroplane flights to have a very successful meeting. It is hoped that the conference proceedings will be available in 1996. J.R. Partington

Quantum Groups and Quantum Spaces.

In November 1995 E.C. Lance attended the first week of a month-long “minisemester” on Quantum Groups and Quantum Spaces at the Banach Center, Warsaw. The first week was devoted to C^{∗}-algebraic aspects of the theory. The hot news there was that Woronowicz (Warsaw) and Masuda (Tsukuba, Japan) have found a set of axioms for locally compact quantum groups. The axioms are satisfied by the function algebras and (reduced) convolution C^{∗}-algebras of all locally compact groups, and also by all known nonclassical C^{∗}-algebraic examples of quantum groups. The axioms give rise to a duality theory extending the Pontryagin duality for locally compact abelian groups. The drawback to the theory at the moment is that one of the axioms postulates the existence of a Haar weight (“noncommutative” analogue of Haar measure). Ideally, this should be a theorem rather than an axiom. J.R. Partington

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. R.J. Archbold (Abdn) and E. Kaniuth, On the primitive ideal space of a finitely generated nilpotent group, to appear in Math. Forum R.J. Archbold (Abdn) and E. Kaniuth, Simply connected nilpotent Lie groups with quasistandard C^{∗}-algebras. R.J. Archbold (Abdn), E. Kaniuth, G. Schlichting and D.W.B. Somerset (Abdn), Ideal spaces of the Haagerup tensor product of C^{∗}-algebras. R.J. Archbold (Abdn) and J.S. Spielberg, Upper and lower multiplicity for irreducible representations of C^{∗}-algebras, II. W.G. Bade, H.G. Dales (LE) and Z.A. Lychova (LA), Algebraic and strong splittings of extensions of Banach algebras J. W. Baker and M. Filali, Minimal ideals in group algebras and their biduals. L. Baratchart, J. Leblond, J.R. Partington (LE) and N. Torkhani, Robust identification in the disc algebra from band-limited data. L. Baratchart, J. Leblond and J.R. Partington (LE), Hardy approximation to L^{∞} functions on subsets of the circle. G. Blower (LA), Stationary processes for Translation Operators, 30 pages, to appear in Proc. London Math. Soc.. G. Blower (LA), Abel means of operator-valued processes, 17 pages, to appear in Studia Mathematica. G. Blower (LA), Quadratic integrals and factorization of linear operators, 18 pages,to appear in J. London Math. Soc.. G. Blower (LA), Multipliers for semigroups, 12 pages, to appear in Proc. Edinburgh Math. Soc.. G. Blower (LA), Complete polynomial bounds for matrices, preprint. A.L.Browni (NCL) & H.L.Vasudeva, The Calculus of Operator Functions, Operator Monotonicity and Operator Convexity. H.G. Dales (LE) and R.J. Loy, Uniqueness of norm for Banach algebras with finite-dimensional radical. P. G. Dixon, Topologically irreducible representations and radicals in Banach algebras. A.P. Donsig (LA) and Alan Hopenwasser, Order Preservation in Limit Algebras, J. of Funct. Anal. (1995) A.P. Donsig (LA) and T.D. Hudson, The Lattice of Ideals of a TAF Algebra, to appear in J. of Funct. Anal.. A.P. Donsig (LA) and J.R. Peters, Nest Algebras with Locally Constant Cocycles, to appear in Proc. London Math. Soc.. N.F. Dudley Ward (LE) and J.R. Partington (LE), Robust identification in the disc algebra using rational wavelets and orthonormal basis functions. N.F. Dudley Ward (LE) and J.R. Partington (LE), A construction of rational wavelets and frames in Hardy-Sobolev spaces with applications to system modelling. J. Eschmeier (LE), H^{∞} functional calculus for spherical contractions. T. Feeman (LA), The Bourgain algebra of a nest algebra. J. J. Green, (research student, Sheffield), Banach algebras of topologically bounded index. D. Heffernan (LA), Uniformly T_{2} algebras in approximately finite-dimensional C^{∗}-algebras, to appear in J. London Math. Soc..

G.J.O. Jameson (LA), Khinchin’s inequality for operators, to appear in Glasgow Math. Jour.. G.J.O. Jameson (LA), 2-convexity and 2-concavity in Schatten ideals, to appear in Math. Proc. Cambridge Phil. Soc.. E.C. Lance (LE), The compact quantum group SO(3)_{q}. A. Moran, (research student, Sheffield), Minimal normal systems in compact right topological groups. J.R. Partington (LE) and P.M. Mäkilä, Modelling of linear fading-memory systems. S.C. Power (LA), K.R.Davidson and V.I.Paulsen, Tree algebras, semidiscreteness and dilation theory, Proc. London Math. Soc. 68 (1994), 178-202. S.C. Power (LA), Infinite lexicographic products of triangular algebras, Bull. London Math. Soc. 27 (1995) 273-277. S.C. Power (LA), Homology for Operator Algebras I : Spectral homology for reflexive algebras J. Functional Analysis, 131 (1995), 29-53. S.C. Power (LA), Lexicographic semigroupoids to appear in J. Ergodic Theory and Dynamical Systems. S.C. Power (LA), Homology for Operator Algebras II : Stable homology for non-self-adjoint algebras, to appear in J. Functional Anal.. S.C. Power (LA), On the Banach space isomorphism type of AF C*-algebras and their triangular subalgebras, to appear in Israel J. Math.. S.C. Power (LA) and C. Laurie, On the C^{∗}-envelope of approximately finite-dimensional operator algebras, to appear in Math. Skand.. S.C. Power (LA) and A. Katavolos, The Fourier Binest Algebra, preprint. S.C. Power (LA), Homology for Operator Algebras III : Partial isometry homotopy and triangular algebras, preprint. S.C. Power (LA) and A.P.Donsig (LA), The failure of approximate inner conjugacy for standard diagonals in regular limit algebras, preprint. S.C. Power (LA) and A.P.Donsig (LA)) Homology for Operator Algebras IV : On the regular classification of limits of 4-cycle algebras, preprint. S.C. Power (LA), Completely contractive representations of some doubly generated antisymmetric operator algebras, preprint J. Pym (Shef) and J. Laali, Concepts of Arens regularity for general measure algebras Quarterly J. Math.. J. Pym (Shef), A. T. Lau and P. Milnes, Locally compact groups, invariant means and the centres of compactifications J. London Math. Soc. P. Quiggin (LA), For which reproducing kernel Hilbert spaces is Pick’s theorem true?, to appear in J. Integral Equations and Operator Theory. D.W.B. Somerset (Abdn), The local multiplier algebra of a C^{∗}-algebra to appear in Quart. J. M. Oxford D.W.B. Somerset (Abdn), The proximinality of the centre of a C^{∗}-algebra D.W.B. Somerset (Abdn), The central Haagerup tensor product of a C^{∗}-algebra M.P. Thomas (LE), Single-element properties in commutative radical Banach algebras: a classification scheme. M.P. Thomas (LE), Closed ideals in the Banach algebra l^{1}(ω) when ω is ϵ-star-shaped. N.J. Young (LA) and V.V. Peller, Superoptimal singular values and indices of matrix functions, Integral Equations and Operator Theory 20 (1994) 350-363. N.J. Young (LA), The spectral Nevanlinna-Pick problem and scalar complex interpolation, Linear Complex Analysis Problem Book, Part 1, Lecture Notes in Math., Springer, Berlin, 1994, no. 1573.

N.J. Young (LA) and V. Peller, Superoptimal analytic approximation of matrix functions, J. Funct. Anal. 120 (1994), 300–343. N.J. Young (LA) and V. Peller, Superoptimal approximation by meromorphic functions, to appear in Math. Proc. Cam. Phil. Soc., 19pp.

RECENT PUBLICATIONS — PAPERS.

R.J. Archbold (Abdn), On residually finite-dimensional C^{∗}-algebras, Proc. Amer. Math. Soc. 123 (1995) 2935-2937. G. Blower (LA), On the stochastic spectral radius formula, Quart. J. Math. Oxford (2), 46 (1995) 1-10. P.G.Dixon, Banach algebras satisfying the non-unital von Neumann inequality, Bull. London Math. Soc., 27 (1995), 359–362. N.F. Dudley Ward (LE) and P.C. Fenton, Some results of Phragmén-Lindelöf type, J. Math. Anal. and Appl. 192 (1995), 63–70. J. Eschmeier (LE) and M. Putinar, The finite fibre problem and an index formula for elementary operators, Proc. Amer. Math. Soc. 123 (1995), 743–746. G.J.O. Jameson (LA), A specific form of Grothendieck’s inequality for the two-dimensional case, with applications to C^{∗}-algebras, Proc. Edinburgh Math. Soc., 37 (1994), 521-537. G.J.O. Jameson (LA), The number of elements required to determine (p,1)-summing norms, Illinois J. Math., 39 (1995) 251-257. Z. Lykova (LA), The homology of C*-algebras, Linear Complex Analysis Problem Book, Part 1, Lecture Notes in Math., Springer, Berlin, 1994, no. 1573, 79-82. P.M. Mäkilä and J.R. Partington (LE), On bounded-error identification of feedback systems, Int. J. Adaptive Control and Sig. Processing 9 (1995), 47–61. J.R. Partington (LE) and P.M. Mäkilä, Worst case analysis of the least squares method and related identification methods, Sys. Control Lett. 24 (1995), 193–200. J.R. Partington (LE) and P.M. Mäkilä, Analysis of linear methods for robust identification in ℓ_{1}, Automatica 31 (1995), 755–758. John Pym (Shef) and A. T. Lau, The topological centre of a compactification of a locally compact group, Math. Z. 219 (1995) 567–579. P.M. Mäkilä, J.R. Partington (LE) and T.K. Gustafsson, Worst-case control-relevant identification, Automatica 31 (1995), 1799–1819.

M.SC. AND PH.D. THESES

Lai Qinsheng, Weighted inequalities for some classical integral operators, Ph.D., University of Leeds, 1995.

Lai Qinsheng is currently working in Edinburgh with Tony Carbery. Jason Clarke, Hilbert C*-modules and their unbounded operators, Ph.D., University of Leeds, 1995.

Jason Clarke has gone to work as a trainee accountant with Arthur Andersen’s. From what he tells ECL, they are keeping him very busy (but paying him a lot!). Martin Wignall, The Laplace Operator on Hyperbolic Space, M.Phil., University of Lancaster. David Heffernan, Some non-self-adjoint Limit Algebras, Ph.D., University of Lancaster.

FORTHCOMING BOOKS

H. Garth Dales and W. Hugh Woodin Super-real fields: totally ordered fields with additional structure, London Mathematical Society Monographs 14, Oxford University Press, xii+356 pp.

This volume was advertised in the January 1994 newsletter as “to appear in 1994”. It will actually appear in March 1996, price 55 pounds, reduced to 41.25 for LMS Members.

J. Eschmeier and M. Putinar Spectral decompositions and analytic sheaves, London Mathematical Society Monographs, 10,

It will be published in February 1996; price 75 pounds, reduced to 56.25 for LMS members.

This book uses the language of homological algebra and sheaf theory to describe recent developments in multivariable spectral theory. Special emphasis is given to applications in several variable complex analysis. Among the topics treated are: Taylor’s analytic functional calculus, spectral decompositions and invariant subspace-results, Toeplitz systems on multivariable Bergman spaces, Fredholm and index theory, quasi-coherent sheaves on Stein spaces, Grauert’s direct image theorem, a Riemann-Roch theorem for complex spaces with singularities.

E.C. Lance Hilbert C*-modules: a toolkit for operator algebraists,

listed as ‘forthcoming’ in last year’s Newsletter, has now appeared (LMS Lecture Note Series 210, CUP, ISBN 0 521 47910).

SOME BOOK REVIEWS AND ABSTRACTS

Michael Guillen Five equations that changed the world (1995) Little, Brown and Co.

The reviewer thinks that this book should be taken seriously, and also believes it to be a cut above the run of ‘popular’ maths books. Guillen totally ignores Hawking’s slogan that ‘each equation will halve the number of sales’. On the contrary, this book specifically deals with five equations (can you guess what they are ?). In my opinion, the book is successful, and the case for these five equations is convincingly made.

But what about Functional Analysis ? Is there an equation in Functional Analysis which has changed the world ? The best I can offer is the equation QP − P Q = aI in quantum physics, which has presumably ”led” to lasers, CD-players etc. This example is perhaps not completely convincing. Can you do better ? R.J. Plymen

BANACH ALGEBRAS THROUGH THE AGES

1. UCLA, LOS ANGELES, California, 1 - 12 July 1974 Title: Homomorphisms and derivations from Banach algebras. Sponsored by Bill Bade and Phil Curtis, with the support of their NSF grant; detailed organization by HGD. Speakers for the first week included W.G.Bade, P.C.Curtis, and S.Scheinburg. Speakers for the second week: H.G.Dales, K.B.Laursen, J.P.McClure, R.T.Moore, M.Thomas, H.Schultz.

[I have lost the full list for the first week] Other people who attended included: R.Arens, A. Browder, F.Dashiell, T.W.Gamelin, S. Grabiner, D.Larson, D. Marshall, A.G.O’Farrell, T.Slobko, J.D.Stein. W.Zelasko

2. University of Leeds, LEEDS, England 14-18 June 1976 Title:Conference on automatic continuity. Sponsored by the UK Science Research Council; a grant of 2500 pounds covered all the costs of travel and accommodation! Organized by HGD. The list of speakers was: G.R.Allan, J.P.R.Christensen, P.C.Curtis, H.G.Dales, P.G.Dixon, J.Esterle, N.Jewell, B.E.Johnson, S. Kaiser, R.J.Loy, J.P.McClure, A.M. Sinclair, M.P.Thomas [I have the notes on all the talks!]

3. California State University, LONG BEACH, California 13-31 July 1981 Title: Commutative radical Banach algebras and automatic continuity. Sponsored by the NSF and Calstate Long Beach. Organized by John Bachar The complete list of participants and the lectures of the speakers are given in the Conference Proceedings, LNM 975.

4. University of Copenhagen, COPENHAGEN, Denmark 15-26 July 1985 Title: Derivations from Banach algebras. Partially supported by the Danish Science Research Counil, with a grant of 17.000 DKK (less than 2000 pounds) Organized by Kjeld Laursen. The participants from outside Denmark included: W.G.Bade, P.C.Curtis, S.Grabiner, M.P.Thomas, J.Bachar, J.Esterle, G.R.Allan, F.Gordeau, H.G.Dales, M.M.Neumann, E.Strouse.

5. University of California, BERKELEY, California. Summer 1986 Title: Workshop on Banach algebras. Sponsored by the NSF through the grant of Bill Bade and Phil Curtis. Exact dates? [Just before the International Congress] Speakers included G.Bachelis, W.G.Bade, P.C.Curtis, H.G.Dales, S. Grabiner, Niels Groenbaek, M.M.Neumann, K.B.Laursen, and M.P.Thomas

6. University of Leeds, LEEDS, England 23 June - 3 July 1987 Title: Automatic continuity and radical Banach algebras. Sponsored by the UK Science Research Council. Organized by H.G.Dales. The list of speakers at the conference was: R.J.Loy, P.C.Curtis, P.G.Dixon, Y.Domar, B. Aupetit, G.R.Allan, K.B.Laursen, E.Strouse, S. Grabiner, F.Zouakia, J.Gale, B.E.Johnson, M.PThomas, A.M.Sinclair, H.G.Dales, M.A. Hennings, A. Paterson, N.Goenbaek, F.Goodman, C.J.Read, W.G.Bade; the semester began on 6 March 1987, and other speakers included E.Albrecht, J.R.Esterle, P.Vrbova, D.Luminet, T.J.Ransford, and J.Rennison.

7. University of California, BERKELEY, CALIFORNIA. 6-22 July 1988 Title: Workshop on Banach algebras. Sponsored by the NSF through the grant of Bill Bade and Phil Curtis. The participants were: G.R.Allan, H.G.Dales, F.Ghahramani, J.P.McClure, K.B.Laursen, N. Groenbaek, S Kilmer, M.M Neumann, M Thomas, S Grabiner, [more???] 8. Australian National University, CANBERRA, AUSTRALIA 2 January-

21 January 1989 Title : Automatic continuity and radical Banach algebras Funded by the Centre for Mathematical Analysis (A$24,000) and a special interest meeting grant from the Australian Mathematical Society (A$2000). Organized by Rick Loy. The participants and the lectures of the speakers are listed in the conference proceedings, Proceedings of the Centre for Mathematical Analysis, 21 (1989).

9. University of California, BERKELEY, CALIFORNIA, 23 July - 3 August 1990 Title : Third Berkeley Banch algebras workshop Sponsored by the NSF through the grant of Bill Bade and Phil Curtis The participants were: G.R.Allan, J.Bachar, H.G.Dales, M.Despic, P.Detre, B.E.Johnson, K.B.Laursen, M.M Neumann, M.P.Thomas, J.Feinstein, J. Gale, F. Ghahramani, S.Grabiner, H.Kamowitz, A.Kitover R.J.Loy, J.P.McClure, V.Ngo, S. Ouzomgi, J.Rennison, J.Stein.

10. University of Cambridge, CAMBRIDGE, England 1- 12 July 1991 Title: Cambridge Banach algebras symposium. Organiser: Graham Allan. partially funded by the London Mathematical Society and the Department of Pure Mathematics. The list of participants that I have now has 45 names

11. University of Manitoba, WINNIPEG, Manitoba, Canada, 3-13 August 1993 Title: Banach algebras and amenability. Organised by Fereidoun Ghahramani and Peter McClure. Partial funding from NSERC The list of participants that I have now has 52 names.

12. University of Newcastle-upon-Tyne, NEWCASTLE, England, 17-28 July 1995 Title: Banach algebras 1995. Organized by Barry Johnson and Michael White. Vast list of participants.

MEMBER UNIVERSITIES, COMMITTEE MEMBERS 1994–5

\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) Dr. T. A. Gillespie, Department of Mathematics and Statistics, James Clerk Maxwell Building, University of Edinburgh, The King’s Buildings, Mayfield Road, EDINBURGH, EH9 3JZ. e-mail: t.a.gillespie@uk.ac.edinburgh Fax: 0131 650 6553 Tel: 0131 650 5081/5060

\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 (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 PMT6JRP@leeds.ac.uk Fax: 0113 242 9925 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 Fax: 0114 282 4292 Tel: 0114 282 4429