Modular Theory in Operator Algebras (Cambridge IISc Series)
Cambridge University Press, 12/3/2020
EAN 9781108489607, ISBN10: 1108489605
Hardcover, 456 pages, 24.6 x 19 x 2.8 cm
Language: English
Originally published in English
The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by Ş.V. Strătilă 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.