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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
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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

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.

• 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