The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces (Memoirs of the American Mathematical Society) by David P. Blecher (PDF)

Description

The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C*$-modules and their maps. Here we give a systematic exposition of this theory. The main part of this memoir consists of a `calculus’ for one-sided $M$-ideals and multipliers, i.e. a collection of the properties of one-sided $M$-ideals and multipliers with respect to the basic constructions met in functional analysis. This is intended to be a reference tool for `noncommutative functional analysts’ who may encounter a one-sided $M$-ideal or multiplier in their work.

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