Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47L05, 46B20

Retrieve articles in all journals with MSC (2000): 47L05, 46B20


Additional Information

T. S. S. R. K. Rao
Affiliation: Statistics and Mathematics Unit, Indian Statistical Institute, R. V. College P.O., Bangalore 560059, India
Email: tss@isibang.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07832-9
PII: S 0002-9939(05)07832-9
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.