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Multivariable Operator Theory on Noncommutative Domains
by
Gelu Popescu
University of Texas San Antonio
We study noncommutative domains Df ⊂ B(H)n generated by positive regular free holomorphic functions f, where B(H) is the algebra of all bounded linear operators on a Hilbert space H. Each such a domain has a universal model (W1, ..., Wn) of weighted shifts acting on the full Fock space with n generators. The study of Df is close related to the study of the weighted shifts W1, ..., Wn, their joint invariant subspaces, and the representations of the algebras they generate: the domain algebra An(Df), the Hardy algebra Fn∞(Df), and the C*-algebra C*(W1, ..., Wn). A good part of the talk deals with these issues. We discuss problems related to the dilation theory, model theory, and unitary invariants on noncommutative domains and noncommutative varieties. Commutant lifting results and applications are also considered.
Date received: May 28, 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 # cawh-63.