Finite von Neumann Algebras and Masas

The first book devoted to the general theory of finite von Neumann algebras.

Allan Sinclair (Author), Roger Smith (Author)

9780521719193, Cambridge University Press

Paperback, published 26 June 2008

410 pages
22.7 x 15.1 x 2.1 cm, 0.56 kg

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

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.

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 ?
Appendix B. Unbounded operators
Appendix C. The trace revisited
Index.

Subject Areas: Calculus & mathematical analysis [PBK]