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

 

Compact Schur multipliers


Author: Milan Hladnik
Journal: Proc. Amer. Math. Soc. 128 (2000), 2585-2591
MSC (2000): Primary 47B07, 47B49; Secondary 46M05, 47L20
Published electronically: February 28, 2000
MathSciNet review: 1766604
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Abstract: Compact Schur multipliers on the algebra $B(\mathcal{H})$ of all bounded linear operators on an infinite-dimensional separable complex Hilbert space $\mathcal{H}$ will be identified as the elements of the Haagerup tensor product $c_0 \otimes^h c_0$ (the completion of $c_0 \otimes c_0$ in the Haagerup norm). Other ideals of Schur multipliers related to compact operators will also be characterized.


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Additional Information

Milan Hladnik
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia
Email: Milan.Hladnik@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05708-7
PII: S 0002-9939(00)05708-7
Keywords: Schur multipliers, compact and weakly compact multipliers, Haagerup tensor products
Received by editor(s): October 7, 1998
Published electronically: February 28, 2000
Additional Notes: This work was supported in part by the Ministry of Science and Technology of Slovenia.
The author expresses his gratitude to Professor Bojan Magajna for a discussion concerning the Haagerup tensor product of $C^{*}$-algebras and for a careful reading of the first version of this paper.
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society