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

TL;DR

This paper systematically develops the theory of one-sided $M$-ideals and multipliers in operator spaces, generalizing classical concepts and providing a reference for noncommutative functional analysts.

Contribution

It offers a comprehensive exposition of one-sided $M$-ideals and multipliers, bridging classical $M$-ideals, operator algebra ideals, and Hilbert $C^*$-modules.

Findings

Unified framework for one-sided $M$-ideals and multipliers

Connections to classical $M$-ideals and operator algebra ideals

Reference tool for noncommutative functional analysis

Abstract

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; a reference tool for `noncommutative functional analysts' who may encounter a one-sided $M$-ideal or multiplier in their work.