Proceedings of the American Mathematical Society

Author(s): Milan Hladnik
Journal: Proc. Amer. Math. Soc. 128 (2000), 2585-2591.
MSC (2000): Primary 47B07, 47B49; Secondary 46M05, 47L20
Posted: February 28, 2000
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B07, 47B49, 46M05, 47L20

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

DOI: 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
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society

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