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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isometries of certain operator spaces


Authors: R. Khalil and A. Saleh
Journal: Proc. Amer. Math. Soc. 132 (2004), 1473-1481
MSC (2000): Primary 46B20; Secondary 46B04
Published electronically: October 3, 2003
MathSciNet review: 2053355
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Abstract: Let $X$ and $Y$ be Banach spaces, and $L(X,Y)$ be the spaces of bounded linear operators from $X$ into $Y.$ In this paper we give full characterization of isometric onto operators of $L(X,Y),$ for a certain class of Banach spaces, that includes $\ell ^{p},$ $1<p<\infty .$ We also characterize the isometric onto operators of $L(c_{0})$ and $K(\ell ^{1}),$the compact operators on $\ell ^{1}.$ Furthermore, the multiplicative isometric onto operators of $L(\ell ^{1})$, when multiplication on $L(\ell ^{1})$ is taken to be the Schur product, are characterized.


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Additional Information

R. Khalil
Affiliation: Department of Mathematics, University of Jordan, Amman 11942, Jordan
Email: roshdi@ju.edu.jo

A. Saleh
Affiliation: Department of Mathematics, King Hussein University, Maan, Jordan

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07210-1
PII: S 0002-9939(03)07210-1
Keywords: Isometries, operator spaces
Received by editor(s): June 17, 2002
Received by editor(s) in revised form: January 14, 2003
Published electronically: October 3, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society