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Isometrically equivalent composition operators on spaces of analytic vector-valued functions

Published online by Cambridge University Press:  01 October 1999

William E. Hornor  and
James E. Jamison
William E. Hornor
Affiliation:
Department of Mathematics, University of Southern Mississippi, Hattiesburg, Mississippi 39406, USA
James E. Jamison
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152, USA
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Abstract

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Let $X$ be a Banach space and let $B(X)$ denote the space of bounded operators on $X$. Two elements $S,T\inB(X)$ are isometrically equivalent if there exists an invertible isometry $V$ such that $TV=VS$. If $X$ is a Hilbert space, then $V$ is a unitary operator and $S$ and $T$ are said to be unitarily equivalent.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 3 , October 1999 , pp. 441 - 451
Copyright
1999 Glasgow Mathematical Journal Trust