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Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class C0

Published online by Cambridge University Press:  20 November 2018

Raphaël Clouâtre
Raphaël Clouâtre*
Affiliation:
Department of Pure Mathematics, University of Waterloo, 200 University Ave. West, Waterloo ON, N2L 3G1. e-mail: rclouatre@uwaterloo.ca
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Abstract

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We obtain results on the unitary equivalence of weak contractions of class ${{C}_{0}}$ to their Jordan models under an assumption on their commutants. In particular, our work addresses the case of arbitrary finite multiplicity. The main tool in this paper is the theory of boundary representations due to Arveson. We also generalize and improve previously known results concerning unitary equivalence and similarity to Jordan models when the minimal function is a Blaschke product.

Keywords

47A4547L55weak contractionsoperators of class C0Jordan modelunitary equivalence
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 1 , 01 February 2015 , pp. 132 - 151
Copyright
Copyright © Canadian Mathematical Society 2015

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