Memoirs of the American Mathematical Society 2006; 85 pp; softcover Volume: 179 ISBN10: 0821838237 ISBN13: 9780821838235 List Price: US$68 Individual Members: US$40.80 Institutional Members: US$54.40 Order Code: MEMO/179/842
 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  Introduction
 Preliminaries
 Spatial action
 Examples
 Constructions
 Onesided 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
