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
DOI:
https://doi.org/10.1090/S0002-9939-04-07340-X
Published electronically:
February 6, 2004
MathSciNet review:
2053985
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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. 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:
https://doi.org/10.1090/S0002-9939-04-07340-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
