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Local isometries of $\mathcal{L}(X,C(K))$

Author: T. S. S. R. K. Rao
Journal: Proc. Amer. Math. Soc. 133 (2005), 2729-2732
MSC (2000): Primary 47L05, 46B20
Published electronically: March 22, 2005
MathSciNet review: 2146220
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Abstract: In this paper we study the structure of local isometries on $\mathcal{L}(X,C(K))$. We show that when $K$ is first countable and $X$ is uniformly convex and the group of isometries of $X^\ast$ is algebraically reflexive, the range of a local isometry contains all compact operators. When $X$ is also uniformly smooth and the group of isometries of $X^\ast$ is algebraically reflexive, we show that a local isometry whose adjoint preserves extreme points is a $C(K)$-module map.

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Additional Information

T. S. S. R. K. Rao
Affiliation: Statistics and Mathematics Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India

Keywords: Isometries
Received by editor(s): March 16, 2004
Received by editor(s) in revised form: May 12, 2004
Published electronically: March 22, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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