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

 

Restricted Schur multipliers and their applications


Author: Timur Oikhberg
Journal: Proc. Amer. Math. Soc. 138 (2010), 1739-1750
MSC (2000): Primary 47B06, 47B10, 47B49, 47L20
Published electronically: January 19, 2010
MathSciNet review: 2587459
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Abstract: We compute the norm of the restriction of a Schur multiplier, arising from a multiplication operator, to a coordinate subspace. This result is used to generalize Wielandt's minimax inequality. Furthermore, we compute various $ s$-numbers of an elementary Schur multiplier and determine criteria for membership of such multipliers in certain operator ideals.


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Additional Information

Timur Oikhberg
Affiliation: Department of Mathematics, University of California - Irvine, Irvine, California 92697 – and – Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: toikhber@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10203-2
PII: S 0002-9939(10)10203-2
Keywords: Schur product, elementary operators, minimax inequalities, $s$-numbers, operator ideals
Received by editor(s): May 3, 2009
Received by editor(s) in revised form: September 2, 2009
Published electronically: January 19, 2010
Additional Notes: The author is grateful to I. Todorov for many stimulating conversations
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society