One-sided M-Ideals and Multipliers in Operator Spaces, I

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 l...

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Bibliographic Details
Published in:arXiv.org 2002-11
Main Authors: Blecher, David P, Effros, Edward G, Zarikian, Vrej
Format: Article
Language:English
Subjects:
Algebra
Banach spaces
Norms
Operators (mathematics)
Subspaces
Online Access:Get full text
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Summary: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.
ISSN:2331-8422