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ON OPERATORS CAUCHY DUAL TO 2-HYPEREXPANSIVE OPERATORS

Published online by Cambridge University Press:  08 January 2008

Sameer Chavan
Sameer Chavan
Affiliation:
Department of Mathematics, University of Pune, Pune 411007, India (sameer\[email protected])
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Abstract

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The operator Cauchy dual to a $2$-hyperexpansive operator $T$, given by $T'\equiv T(T^*T)^{-1}$, turns out to be a hyponormal contraction. This simple observation leads to a structure theorem for the $C^*$-algebra generated by a $2$-hyperexpansion, and a version of the Berger–Shaw theorem for $2$-hyperexpansions.

As an application of the hyperexpansivity version of the Berger–Shaw theorem, we show that every analytic $2$-hyperexpansive operator with finite-dimensional cokernel is unitarily equivalent to a compact perturbation of a unilateral shift.

Keywords

Primary 47B20hyponormal contraction2-hyperexpansive operatorCauchy dual
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 637 - 652
Copyright
Copyright © Edinburgh Mathematical Society 2007