Modular theory in operator algebras / Serban Valentin Strătilă.

Format:

Book

Author/Creator:

Str̆atil̆a, Şerban Valentin, 1943- author.

Series:

Cambridge - IISc series.

Cambridge - IISc series

Language:

English

Subjects (All):

Operator algebras.

Physical Description:

1 online resource (xii, 447 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2020.

Summary:

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.

Contents:

Cover

Modular Theory in Operator Algebras

Series

Title

Copyright

Dedication

Contents

Preface to the Second Edition

Preface to the First Edition

CHAPTER I Normal Weights

1 Characterizations of Normality

2 The Standard Representation

3 The Balanced Weight

4 The Pedersen-Takesaki Construction

5 The Converse of the Connes Theorem

6 Equality and Majorization of Weights

7 The Spatial Derivative

8 Tensor Products

CHAPTER II Conditional Expectations and Operator-Valued Weights

9 Conditional Expectations

10 Existence and Uniqueness of Conditional Expectations

11 Operator-Valued Weights

12 Existence and Uniqueness of Operator-Valued Weights

CHAPTER III Groups of Automorphisms

13 Groups of Isometries on Banach Spaces

14 Spectra and Spectral Subspaces

15 Continuous Actions on W∗-algebras

16 The Connes Invariant ( )

17 Outer Automorphisms

CHAPTER IV Crossed Products

18 Hopf-von Neumann Algebras

19 Crossed Products

20 Comparison of cocycles

21 Abelian Groups

22 Discrete Groups

CHAPTER V Continuous Decompositions

23 Dominant Weights and Continuous Decompositions

24 The Flow of Weights

25 The Fundamental Homomorphism

26 The Extension of the Modular Automorphism Group

CHAPTER VI Discrete Decompositions

27 The Connes Invariant T( )

28 The Connes Invariant S( )

29 Factors of Type III (0 ≤ &lt

1)

30 The Discrete Decomposition of Factors of Type III (0 ≤ &lt

Appendix

References

Notation Index

Subject Index.

Notes:

First edition published by Editura Academiei and Abacus Press, 1981.

Title from publisher's bibliographic system (viewed on 29 Oct 2020).

Includes bibliographical references (pages 429-442) and indexes.

Other Format:

Print version:

ISBN:

1-108-96677-2

1-108-77903-4

9781108779036

1108779034

OCLC:

1202672504