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The Calculus of One-Sided \(M\)-Ideals and Multipliers in Operator Spaces
David P. Blecher, University of Houston, TX, and Vrej Zarikian, University of Cincinnati, OH

Memoirs of the American Mathematical Society
2006; 85 pp; softcover
Volume: 179
ISBN-10: 0-8218-3823-7
ISBN-13: 978-0-8218-3823-5
List Price: US$68
Individual Members: US$40.80
Institutional Members: US$54.40
Order Code: MEMO/179/842
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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

  • Introduction
  • Preliminaries
  • Spatial action
  • Examples
  • Constructions
  • One-sided type decompositions and Morita equivalence
  • Central \(M\)-structure for operator spaces
  • Future directions
  • Appendix A. Some results from Banach space theory
  • Appendix B. Infinite matrices over an operator space
  • Appendix. Bibliography
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