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  1. Home
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  3. Finite von Neumann Algebras and Masas
  • Cited by 43
Publisher:
Cambridge University Press
Online publication date:
May 2010
Print publication year:
2008
Online ISBN:
9780511666230
DOI:
https://doi.org/10.1017/CBO9780511666230
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
London Mathematical Society Lecture Note Series (351)
Information

Book description

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.

Reviews

'Sinclair and Smith's monograph is very well written … well suited for graduate students who have been given a first course on operator algebras, for Ph.D. students who have started working on finite von Neumann algebras, but also for specialists because it gathers much useful and technical material.'

Source: Mathematical Reviews

'… suitable for graduate students wanting to learn this part of mathematics.'

Source: EMS Newsletter

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