Finite von Neumann algebras and masas / Allan M. Sinclair, Roger R. Smith.

Format:

Book

Author/Creator:

Sinclair, Allan M., author.

Smith, Roger R., author.

Series:

London Mathematical Society lecture note series ; 351.

London Mathematical Society lecture note series ; 351

Language:

English

Subjects (All):

Von Neumann algebras.

Physical Description:

1 online resource (ix, 400 pages) : digital, PDF file(s).

Other Title:

Finite von Neumann Algebras & Masas

Place of Publication:

Cambridge : Cambridge University Press, 2008.

Language Note:

English

Summary:

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.

Contents:

General introduction

Masas in B(H)

Finite von Neumann algebras

The basic construction

Projections and partial isometries

Normalisers, orthogonality, and distances

The Pukanszky invariant

Operators in L

Perturbations

General perturbations

Singular masas

Existence of special masas

Irreducible hyperfinite subfactors

Maximal injective subalgebras

Masas in non-separable factors

Singly generated II1 factors

Appendix A. The ultrapower and property GAMMA

Appendix B. Unbounded operators

Appendix C

The trace revisited

Index.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and indexes.

ISBN:

1-139-88561-8

1-107-36795-6

1-107-37248-8

1-107-36304-7

1-107-36906-1

1-299-40554-1

1-107-36549-X

0-511-89415-5

0-511-66623-3