Electronic ISBN:  9781470404437 
Product Code:  MEMO/179/842.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 179; 2006; 85 ppMSC: Primary 46;
The theory of onesided \(M\)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 onesided \(M\)ideals and multipliers, i.e. a collection of the properties of onesided \(M\)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 onesided \(M\)ideal or multiplier in their work.

Table of Contents

Chapters

1. Introduction

2. Preliminaries

3. Spatial action

4. Examples

5. Constructions

6. Onesided type decompositions and Morita equivalence

7. Central $M$structure for operator spaces

8. Future directions


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The theory of onesided \(M\)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 onesided \(M\)ideals and multipliers, i.e. a collection of the properties of onesided \(M\)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 onesided \(M\)ideal or multiplier in their work.

Chapters

1. Introduction

2. Preliminaries

3. Spatial action

4. Examples

5. Constructions

6. Onesided type decompositions and Morita equivalence

7. Central $M$structure for operator spaces

8. Future directions