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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 a 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.

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Book Details

ISBN: 9780521719193
ISBN-10: 0521719194
Format: Paperback
(228mm x 152mm x 21mm)
Pages: 410
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 26-Jun-2008
Country of Publication: United Kingdom

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Author Biography - Allan M. Sinclair

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.

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