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Some remarks on the dilation theory for commuting d-contractions
by
Stefan Richter
University of Tennessee
Coauthors: Carl Sundberg
A family in the sense of J. Agler's model theory is a collection of Hilbert space operators which is uniformly bounded in operator norm and closed under the formation of direct sums, restrictions to invariant subspaces, and unital *-representations. An extremal in a family is an operator that can only be extended to another operator in the family by taking direct sums. It is Agler's theorem that every operator in a family can be extended to an extremal for that family. Based on this, one can give quick proofs of basic extension and dilation theorems. For example every isometric operator has a unitary extension, every contraction has a co-isometric extension, etc. In this talk I will discuss some applications of the model theory in the multi-variable context.
Date received: February 8, 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-35.