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

David P. Blecher University of Houston, Houston, TX
Vrej Zarikian University of Cincinnati, Cincinnati, OH
Available Formats:
Electronic ISBN: 978-1-4704-0443-7
Product Code: MEMO/179/842.E
List Price: $68.00 MAA Member Price:$61.20
AMS Member Price: $40.80 Click above image for expanded view The Calculus of One-Sided$M$-Ideals and Multipliers in Operator Spaces David P. Blecher University of Houston, Houston, TX Vrej Zarikian University of Cincinnati, Cincinnati, OH Available Formats:  Electronic ISBN: 978-1-4704-0443-7 Product Code: MEMO/179/842.E  List Price:$68.00 MAA Member Price: $61.20 AMS Member Price:$40.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 1792006; 85 pp
MSC: Primary 46;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Spatial action
• 4. Examples
• 5. Constructions
• 6. One-sided type decompositions and Morita equivalence
• 7. Central $M$-structure for operator spaces
• 8. Future directions
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Volume: 1792006; 85 pp
MSC: Primary 46;

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.

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Spatial action
• 4. Examples
• 5. Constructions
• 6. One-sided type decompositions and Morita equivalence
• 7. Central $M$-structure for operator spaces
• 8. Future directions
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