《C*代數和W*代數(英文版)》是Springer經典數學教材系列之一。該系列包含已出版的400多本教材，許多已經被奉為經典並該科目的標準參考書。該書對von Neumann代數理論給出了全面而詳細的介紹。幾乎包含該科目的所有基本結果。對於初學著和專家來說《C*代數和W*代數(英文版)》都是一本非常難得的參考書。讀者對象：數學專業的研究生和相關專業的科研人員。
基本介紹
- 書名：C*代數和W*代數
- 作者：章一郎堺
- 出版日期：2009年6月1日
- 語種：英語
- ISBN：9787510004704
- 外文名：C*-algebras and W*-algebras
- 出版社：世界圖書出版公司
- 頁數：256頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《C*代數和W*代數(英文版)》由世界圖書出版公司出版。
作者簡介
作者：(日本)章一郎堺
圖書目錄
1.General Theory
1.1.Definitions of C*-Algebras and W*-Algebras
1.2.Commutative C*-Algebras
1.3.Stonean Spaces
1.4.Positive Elements of a C*-Algebra
1.5.Positive Linear Functionais on a C*-Algebra
1.6.Extreme Points in the Unit Sphere of a C*-Algebra
1.7.The Weak Topology on a W*-Algebra
1.8.Various Topologies on a W*-Algebra
1.9.Kaplansky's Density Theorem
1.10.Ideals in a W*-Algebra
1.11.Spectral Resolution ofSelf-Adjoint Elements in a W*-Algebra
1.12.The Polar Decomposition of Elements of a W*-Algebra
1.13.Linear Functionals on a W*-Algebra
1.14.Polar Decomposition of Linear Functionals on a W*-Algebra
1.15.Concrete C*-Algebras and W*-Algebras
1.16.The Representation Theorems for C*-Algebras and W*- Algebras
1.17.The Second Dual of a O-Algebra
1.18.Commutative W*-Algebras ..
1.19.The C*-Algebra C of all Compact Linear Operators on a Hilbert Space
1.20.The Commutation Theorem of yon Neumann
1.21.*-Representations of C*-Algebras, 1
1.22.Tensor Products of C*-Algebras and W*-Algebras
1.23.The Inductive Limit and Infinite Tensor Product of C*-Algebras
1.24.Radon-Nikodym Theorems in W*-Algebras
2.Classification of W*-Algebras
2.1.Equivalence of Projections and the Comparability Theorem.
2.2.Classification of W*-Algebras
2.3.Type I W*-Algebras.
2.4.Finite W*-Algebras
2.5.Traces and Criterions of Types
2.6.Types of Tensor Products of W*-Algebras
2.7.*-Representations of C*-Algebras and W*-Algebras, 2.
2.8.The Commutation Theorem of Tensor Products
2.9.Spatial Isomorphisms of W*-Algebras
3.Decomposition Theory
3.1.Decompositions of States (Non-Separable Cases)
3.2.Reduction Theory (Space-Free)
3.3.Direct Integral of Hilbert Spaces
3.4.Decomposition of States (Separable Cases)
3.5.Central Decomposition of States (Separable Cases)
4.Special Topics
4.1.Derivations and Automorphisms of C*-Algebras and W*- Algebras
4.2.Examples of Factors, 1 (General Construction)
4.3.Examples of Factors, 2 (Uncountable Families of Types II1,II and III
4.4.Examples of Factors, 3 (Other Results and Problems)
4.5.Global W*-Algebras (Non-Factors)
4.6.Type I C*-Algebras
4.7.On a Stone-Weierstrass Theorem for C*-Algebras
Bibliography
Subject Index
List of Symbols
1.1.Definitions of C*-Algebras and W*-Algebras
1.2.Commutative C*-Algebras
1.3.Stonean Spaces
1.4.Positive Elements of a C*-Algebra
1.5.Positive Linear Functionais on a C*-Algebra
1.6.Extreme Points in the Unit Sphere of a C*-Algebra
1.7.The Weak Topology on a W*-Algebra
1.8.Various Topologies on a W*-Algebra
1.9.Kaplansky's Density Theorem
1.10.Ideals in a W*-Algebra
1.11.Spectral Resolution ofSelf-Adjoint Elements in a W*-Algebra
1.12.The Polar Decomposition of Elements of a W*-Algebra
1.13.Linear Functionals on a W*-Algebra
1.14.Polar Decomposition of Linear Functionals on a W*-Algebra
1.15.Concrete C*-Algebras and W*-Algebras
1.16.The Representation Theorems for C*-Algebras and W*- Algebras
1.17.The Second Dual of a O-Algebra
1.18.Commutative W*-Algebras ..
1.19.The C*-Algebra C of all Compact Linear Operators on a Hilbert Space
1.20.The Commutation Theorem of yon Neumann
1.21.*-Representations of C*-Algebras, 1
1.22.Tensor Products of C*-Algebras and W*-Algebras
1.23.The Inductive Limit and Infinite Tensor Product of C*-Algebras
1.24.Radon-Nikodym Theorems in W*-Algebras
2.Classification of W*-Algebras
2.1.Equivalence of Projections and the Comparability Theorem.
2.2.Classification of W*-Algebras
2.3.Type I W*-Algebras.
2.4.Finite W*-Algebras
2.5.Traces and Criterions of Types
2.6.Types of Tensor Products of W*-Algebras
2.7.*-Representations of C*-Algebras and W*-Algebras, 2.
2.8.The Commutation Theorem of Tensor Products
2.9.Spatial Isomorphisms of W*-Algebras
3.Decomposition Theory
3.1.Decompositions of States (Non-Separable Cases)
3.2.Reduction Theory (Space-Free)
3.3.Direct Integral of Hilbert Spaces
3.4.Decomposition of States (Separable Cases)
3.5.Central Decomposition of States (Separable Cases)
4.Special Topics
4.1.Derivations and Automorphisms of C*-Algebras and W*- Algebras
4.2.Examples of Factors, 1 (General Construction)
4.3.Examples of Factors, 2 (Uncountable Families of Types II1,II and III
4.4.Examples of Factors, 3 (Other Results and Problems)
4.5.Global W*-Algebras (Non-Factors)
4.6.Type I C*-Algebras
4.7.On a Stone-Weierstrass Theorem for C*-Algebras
Bibliography
Subject Index
List of Symbols
