Lectures on Von Neumann Algebras

ISBN-13: 9781108496841 / Angielski / Twarda / 2019 / 438 str.

Serban-Valentin Stratila;Laszlo Zsido (Universita degli Studi di

Opis

Written in lucid language, this valuable text discusses fundamental concepts of von Neumann algebras including bounded linear operators in Hilbert spaces, finite von Neumann algebras, linear forms on algebra of operators, geometry of projections and classification of von Neumann algebras in an easy to understand manner. The revised text covers new material including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras with a cyclic and separating vector. Pedagogical features including solved problems and exercises are interspersed throughout the book.

Spis treści

Preface; Introduction; Dedication; 1. Topologies on spaces of operators; 2. Bounded linear operators in Hilbert space; 3. Von Neumann algebras; 4. The geometry of projections and the classification of von Neumann algebras; 5. Linear forms on operator algebras; 6. Relationships between a von Neumann algebras and its commutant; 7. Finite von Neumann algebras; 8. Spatial isomorphisms and relations between topologies; 9. Unbounded linear operators in Hilbert spaces; 10. The theory of standard von Neumann algebras; Appendix; References; Subject index; Notation index.