MODULAR THEORY IN OPERATOR ALGEBRAS.

✍ Scribed by SERBAN VALENTIN STRATILA

• Publisher: CAMBRIDGE UNIV PRESS US
• Year: 2021
• Tongue: English
• Leaves: 460
• Edition: 2
• Category: Library

✦ Table of Contents

Copyright
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 Γ(𝜎)
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(ℳ)
28 The Connes Invariant S(ℳ)
29 Factors of Type III𝜆 (0 ≤ 𝜆 < 1)
30 The Discrete Decomposition of Factors of Type III𝜆 (0 ≤ 𝜆 < 1)
Appendix
References
Notation Index
Subject Index