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

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**133**(2005), 2729-2732 Request permission

## 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.## References

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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
- MR Author ID: 225502
- ORCID: 0000-0003-0599-9426
- Email: tss@isibang.ac.in
- 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
- © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**133**(2005), 2729-2732 - MSC (2000): Primary 47L05, 46B20
- DOI: https://doi.org/10.1090/S0002-9939-05-07832-9
- MathSciNet review: 2146220