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One-sided
M-Ideals and multipliers in
operator spaces, I
David P. Blecher, Edward G. Effros and Vrej Zarikian |
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Vol. 206 (2002), No. 2, 287–319
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Abstract |
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The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the matrix norms. In turn this is used to prove that the algebra of left adjointable mappings of a dual operator space X is a von Neumann algebra. If in addition X is an operator A–B-bimodule for C∗-algebras A and B, then the module operations on X are automatically weak∗ continuous. One sided L-projections are introduced, and analogues of various results from the classical theory are proved. An assortment of examples is considered. |
Milestones
Received: 18 December 2000
Revised: 13 April 2001
Published: 1 October 2002
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Authors |
| David P. Blecher | |
| Department of Mathematics University of Houston Houston, TX 77204-3008 |
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| Edward G. Effros | |
| Department of Mathematics University of California Los Angeles, CA 90095-1555 |
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| Vrej Zarikian | |
| Department of Mathematics The University of Texas at Austin Austin, TX 78712-1082 |
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