Finite von Neumann Algebras and Masas

by Allan Sinclair, Roger Smith

Overview

A thorough account of the methods that underlie the theory of subalgebras of finite von Neumann algebras, this book contains a substantial amount of current research material and is ideal for those studying operator algebras. The conditional expectation, basic construction and perturbations within a finite von Neumann algebra with a fixed faithful normal trace are discussed in detail. The general theory of maximal abelian self-adjoint subalgebras (masas) of separable II1 factors is presented with illustrative examples derived from group von Neumann algebras. The theory of singular masas and Sorin Popa’s methods of constructing singular and semi-regular masas in general separable II1 factor are explored. Appendices cover the ultrapower of an II1 factor and the properties of unbounded operators required for perturbation results. Proofs are given in considerable detail and standard basic examples are provided, making the book understandable to postgraduates with basic knowledge of von Neumann algebra theory.

Product Details

ISBN-13:	9780521719193
Publisher:	Cambridge University Press
Publication date:	06/26/2008
Series:	London Mathematical Society Lecture Note Series , #351
Pages:	410
Product dimensions:	5.90(w) x 8.90(h) x 1.00(d)

About the Author

Allan M. Sinclair is a Professor Emeritus in the School of Mathematics at the University of Edinburgh.

Roger R. Smith is a Professor in the Department of Mathematics at Texas A&M University.

Table of Contents

General introduction; 1. Masas in B(H); 2. Finite von Neumann algebras; 3. The basic construction; 4. Projections and partial isometries; 5. Normalisers, orthogonality, and distances; 6. The Pukánszky invariant; 7. Operators in L; 8. Perturbations; 9. General perturbations; 10. Singular masas; 11. Existence of special masas; 12. Irreducible hyperfinite subfactors; 13. Maximal injective subalgebras; 14. Masas in non-separable factors; 15. Singly generated II1 factors; Appendix A. The ultrapower and property Γ; Appendix B. Unbounded operators; Appendix C. The trace revisited; Index.

Editorial Reviews

"Sinclair and Smith's monograph is very well written..."
Paul Jolissaint, Mathematical Reviews

From the Publisher