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Look Inside Modular Theory in Operator Algebras

Modular Theory in Operator Algebras

Part of Cambridge IISc Series

Author: Şerban Valentin Strătilă, Institute of Mathematics of the Romanian Academy, Romania

Date Published: December 2020
availability: Available
format: Hardback
isbn: 9781108489607

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About the Authors

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.
- Covers H. Kosaki's extension of the index to arbitrary factors and F. Rădulescu's examples of non-hyperfinite factors of type IIIλ, λ ∈ (0,1) and of type III1
- Explains the group-measure space construction in detail
- Discusses the main aspects of modular theory with complete proofs
- Makes the theory accessible to readers having elementary training in operator algebras
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Product details
- Date Published: December 2020
- format: Hardback
- isbn: 9781108489607
- length: 456 pages
- dimensions: 247 x 190 x 27 mm
- weight: 0.92kg
- availability: Available
Table of Contents
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.
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Author
Şerban Valentin Strătilă, Institute of Mathematics of the Romanian Academy, Romania
Şerban Valentin Strătilă is Professor at the Institute of Mathematics, Romanian Academy, and at the Department of Mathematics, University of Bucharest, Romania. His current research areas include operator algebras and representation theory. He received the 1975 Simion Stoilow Prize for Mathematics by the Romanian Academy. He has published Lectures on von Neumann Algebras, 2nd edition (2019) with Cambridge University Press.