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

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

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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

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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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