One-sided M-Ideals and Multipliers in Operator Spaces, I
Operator Algebras
2007-05-23 v2 Functional Analysis
Abstract
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 -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.
Cite
@article{arxiv.math/0012105,
title = {One-sided M-Ideals and Multipliers in Operator Spaces, I},
author = {David P. Blecher and Edward G. Effros and Vrej Zarikian},
journal= {arXiv preprint arXiv:math/0012105},
year = {2007}
}