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 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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

Author(s): William D. Banks; Asma Harcharras
Journal: Proc. Amer. Math. Soc. 132 (2004), 2121-2125.
MSC (2000): Primary 47A30; Secondary 47B49, 47B10
Posted: February 6, 2004
MathSciNet review: 2053985
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Abstract | References | Similar articles | Additional information

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 $1$.

References:

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J. Bergh and J. Löfström, Interpolation spaces: An introduction, Grundlehren der Mathematischen Wissenschaften, Band 223, Springer-Verlag, Berlin-New York, 1976. MR 58:2349

2.
L. Livshits, A note on $0$-$1$ Schur multipliers, Linear Algebra Appl. 222 (1995), 15-22. MR 96d:15040

3.
I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfadjoint operators, Translations of Mathematical Monographs, Vol. 18, American Mathematical Society, Providence, R.I., 1969. MR 39:7447

4.
R. Schatten, Norm ideals of completely continuous operators, Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 27, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 22:9878

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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: 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
Posted: February 6, 2004
Additional Notes: The first author was supported in part by NSF grant DMS-0070628
Communicated by: Andreas Seeger
Copyright of article: Copyright 2004, American Mathematical Society




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