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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
Posted:
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  lies sufficiently close to  , then it is necessarily equal to  . We also give a simple characterization of those idempotent Schur multipliers on  whose norm is  .
- 1.
Jöran
Bergh and Jörgen
Löfström, Interpolation spaces. An introduction,
Springer-Verlag, Berlin, 1976. Grundlehren der Mathematischen
Wissenschaften, No. 223. MR 0482275
(58 #2349)
- 2.
Leo
Livshits, A note on 0-1 Schur multipliers, Linear Algebra
Appl. 222 (1995), 15–22. MR 1332920
(96d:15040), http://dx.doi.org/10.1016/0024-3795(93)00268-5
- 3.
I.
C. Gohberg and M.
G. Kreĭn, Introduction to the theory of linear
nonselfadjoint operators, Translated from the Russian by A. Feinstein.
Translations of Mathematical Monographs, Vol. 18, American Mathematical
Society, Providence, R.I., 1969. MR 0246142
(39 #7447)
- 4.
Robert
Schatten, Norm ideals of completely continuous operators,
Ergebnisse der Mathematik und ihrer Grenzgebiete. N. F., Heft 27,
Springer-Verlag, Berlin, 1960. MR 0119112
(22 #9878)
- 1.
- 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
 - 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:
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
Posted:
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
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