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# Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class $C_0$

Published:2013-11-26
Printed: Feb 2015
• Raphaël Clouâtre,
Department of Mathematics, Indiana University, 831 East 3rd Street, Bloomington, IN 47405, USA
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## Abstract

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 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: weak contractions, operators of class $C_0$, Jordan model, unitary equivalence
 MSC Classifications: 47A45 - Canonical models for contractions and nonselfadjoint operators 47L55 - Representations of (nonselfadjoint) operator algebras

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