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The left tangential operator-argument interpolation problem on the noncommutative ball
by
Quanlei Fang
Department of Mathematics, Virginia Tech
Coauthors: Joseph A. Ball
We introduce and study a Fock-space noncommutative analogue of reproducing kernel Hilbert spaces (NRKHS) of de Branges-Rovnyak type. The NRKHS based on the noncommutative Szegö kernel is the unsymmetrized Fock space. The noncommutative Schur multiplier class consists of contractive multipliers between two such vector-valued Fock spaces. Popescu and others have studied the left tangential operator-argument interpolation problem for such Schur multipliers via the commutant lifting approach. We discuss how the grassmannian approach to interpolation due to Ball-Helton can be adapted to arrive at a parametrization of the set of all solutions of such a problem. The main tool is an indefinite-metric analogue of recent work of Ball, Bolotnikov and the speaker on Fock Space.
Date received: February 20, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-67.