Finite von Neumann algebras and masas

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 vonNeumann 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 propertiesof unbounded operators required for perturbation results. Proofs are given inconsiderable detail and standard basic examples are provided, making the bookunderstandable to postgraduates with basic knowledge of von Neumann algebra theory. First book devoted to the general theory of finite von Neumann algebras. Contains large amount of current research, yet accessible to any postgraduate student in the area of operator algebras. Detailed discussion of masas, a topic not previously discussed in book form INDICE: 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. Maximalinjective subalgebras; 14. Masas in non-separable factors; 15. Singly generated II1 factors; Appendix A. The ultrapower and property G; Appendix B. Unbounded operators; Appendix C. The trace revisited; Index

• ISBN: 978-0-521-71919-3
• Editorial: Cambridge University Press
• Encuadernacion: Rústica
• Páginas: 410
• Fecha Publicación: 26/06/2008
• Nº Volúmenes: 1
• Idioma: Inglés