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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
Front Cover for The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces
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
Front Cover for The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces
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  • Front Cover for The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces
  • Back Cover for The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces
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.

  • Table of Contents
     
     
    • 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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