The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces

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.