UID:
almafu_9960118621402883
Format:
1 online resource (xii, 447 pages) :
,
digital, PDF file(s).
Edition:
Second edition.
ISBN:
1-108-96677-2
,
1-108-77903-4
,
9781108779036
,
1108779034
Series Statement:
Cambridge - IISc series
Content:
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.
Note:
First edition published by Editura Academiei and Abacus Press, 1981.
,
Title from publisher's bibliographic system (viewed on 29 Oct 2020).
,
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 ≤ < -- 1) -- 30 The Discrete Decomposition of Factors of Type III (0 ≤ < -- 1) -- Appendix -- References -- Notation Index -- Subject Index.
Additional Edition:
ISBN 1-108-48960-5
Additional Edition:
Print version: ISBN 9781108489607
Language:
English
URL:
https://doi.org/10.1017/9781108489607
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