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

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 $C^{\ast }$-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.

Cited by in corpus (8)

• Real operator spaces and operator algebras
• Duality and operator algebras
• Open partial isometries and positivity in operator spaces
• Stable isomorphism of dual operator spaces
• Injective cogenerators among operator bimodules
• Operator spaces which are one-sided M-Ideals in their bidual
• Hilbert modules, rigged modules and stable isomorphism
• Multipliers between two operator spaces