A Commutant Lifting Theorem for a Domain in C^2 and
Spectral Interpolation
Jim Agler and Nicholas Young
Keywords
mu-synthesis, interpolation
Status
Appeared in J. Functional Analysis 161(1999) 452-477.
Abstract
We characterise the pairs of commuting operators on Hilbert
space for which the {\em symmetrised bidisc}, defined to be the set
$$
\Gamma=\{(\lambda_1 +
\lambda_2,\ \lambda_1\lambda_2): |\lambda_1|\le 1,\
|\lambda_2|\le 1\}
$$
is a complete spectral set. We give an application to the
spectral Nevanlinna-Pick problem: we obtain a necessary
condition for the existence of an analytic $2\times 2$ matrix
function satisfying interpolation conditions and bounds on
eigenvalues.
J. Agler's work is suported by an NSF grant in Modern Analysis.
This work was also supported by NATO Collaborative grant CRG 971129
Nicholas Young
25th October 1999.