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

 

On the norm of an idempotent Schur multiplier on the Schatten class


Authors: William D. Banks and Asma Harcharras
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2121-2125
MSC (2000): Primary 47A30; Secondary 47B49, 47B10
Published electronically: February 6, 2004
MathSciNet review: 2053985
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Abstract: We show that if the norm of an idempotent Schur multiplier on the Schatten class $S^p$ lies sufficiently close to $1$, then it is necessarily equal to $1$. We also give a simple characterization of those idempotent Schur multipliers on $S^p$ whose norm is $1$.


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Additional Information

William D. Banks
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: bbanks@math.missouri.edu

Asma Harcharras
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: harchars@math.missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07340-X
PII: S 0002-9939(04)07340-X
Keywords: Idempotent Schur multiplier, Schatten class
Received by editor(s): December 12, 2002
Received by editor(s) in revised form: April 21, 2003
Published electronically: February 6, 2004
Additional Notes: The first author was supported in part by NSF grant DMS-0070628
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society