C-Algebras and W-Algebras

By: Shoichiro Sakai

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Paperback | 1 December 1997

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276 Pages

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23.5 x 15.5 x 1.91

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From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." (Math. Reviews) "In theory, this book can be read by a well-trained third-year graduate student - but the reader had better have a great deal of mathematical sophistication. The specialist in this and allied areas will find the wealth of recent results and new approaches throughout the text especially rewarding." (American Scientist) "The title of this book at once suggests comparison with the two volumes of Dixmier and the fact that one can seriously make this comparison indicates that it is a far more substantial work that others on this subject which have recently appeared"(BLMSoc)

Industry Reviews

From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." (Math. Reviews) "In theory, this book can be read by a well-trained third-year graduate student - but the reader had better have a great deal of mathematical sophistication. The specialist in this and allied areas will find the wealth of recent results and new approaches throughout the text especially rewarding." (American Scientist) "The title of this book at once suggests comparison with the two volumes of Dixmier and the fact that one can seriously make this comparison indicates that it is a far more substantial work than others on this subject which have recently appeared"(BLMSoc)

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General Theory
Definitions of C-Algebras and W-Algebras	p. 1
Commutative C*-Algebras	p. 3
Stonean Spaces	p. 6
Positive Linear Functions on a C*-Algebra	p. 7
Positive Linear Functionals on a C*-Algebra	p. 9
Extreme Points in the Unit Sphere of a C*-Algebra	p. 10
The Weak Topology on a W*-Algebra	p. 14
Various Topologies on a W*-Algebra	p. 19
Kaplansky's Density Theorem	p. 22
Ideals in a W*-Algebra	p. 24
Spectral Resolution of Self-Adjoint Elements in a W*-Algebra	p. 26
The Polar Decomposition of Elements of a W*-Algebra	p. 27
Linear Functionals on a W*-Algebra	p. 28
Polar Decomposition of Linear Functionals on a W*-Algebra	p. 31
Concrete C-Algebras and W-Algebras	p. 33
The Representation Theorems for C-Algebras and W-Algebras	p. 40
The Second Dual of a C*-Algebra	p. 42
Commutative W*-Algebras	p. 45
The C*-Algebra C(H) of all Compact Linear Operators on a Hilbert Space H	p. 46
The Commutation Theorem of von Neumann	p. 48
-Representations of C-Algebras, 1	p. 50
Tensor Products of C-Algebras and W-Algebras	p. 58
The Inductive Limit and Infinite Tensor Product of C*-Algebras	p. 70
Radon-Nikodym Theorems in W*-Algebras	p. 75
Classification of W*-Algebras
Equivalence of Projections and the Comparability Theorem	p. 79
Classification of W*-Algebras	p. 83
Type I W*-Algebras	p. 87
Finite W*-Algebras	p. 89
Traces and Criterions of Types	p. 95
Types of Tensor Products of W*-Algebras	p. 98
-Representations of C-Algebras and W*-Algebras, 2	p. 102
The Commutation Theorem of Tensor Products	p. 108
Spatial Isomorphisms of W*-Algebras	p. 111
Decomposition Theory
Decompositions of States (Non-Separable Cases)	p. 121
Reduction Theory (Space-Free)	p. 131
Direct Integral of Hilbert Spaces	p. 137
Decomposition of States (Separable Cases)	p. 140
Central Decomposition of States (Separable Cases)	p. 146
Special Topics
Derivations and Automorphisms of C-Algebras and W-Algebras	p. 153
Examples of Factors, 1 (General Construction)	p. 171
Examples of Factors, 2 (Uncountable Families of Types II[subscript 1], [actual symbol not reproducible] and III	p. 183
Examples of Factors, 3 (Other Results and Problems)	p. 202
Global W*-Algebras (Non-Factors)	p. 216
Type I C*-Algebras	p. 219
On a Stone-Weierstrass Theorem for C*-Algebras	p. 236
Bibliography	p. 243
Subject Index	p. 251
List of Symbols	p. 255
Table of Contents provided by Blackwell. All Rights Reserved.

C*-Algebras and W*-Algebras

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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C-Algebras and W-Algebras