Modular Theory in Operator Algebras

Discusses the fundamentals and latest developments in operator algebras, focusing on continuous and discrete decomposition of factors of type III.

?erban Valentin Str?til? (Author)

9781108489607, Cambridge University Press

Hardback, published 3 December 2020

456 pages
24.7 x 19 x 2.7 cm, 0.92 kg

The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by ?.V. Str?til? and L. Zsidó) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.

Preface to the second edition
Preface to the first edition
1. Normal weights
2. Conditional expectations and operator valued weights
3. Groups of automorphisms
4. Crossed products
5. Continuous decompositions
6. Discrete decompositions
Appendix
References
Subject Index
Notation Index.

Subject Areas: Algebra [PBF], Mathematics [PB], Mathematics & science [P]