C*代数和W*代数

出版时间：2009-6  出版社：世界图书出版公司  作者：章一郎堺  页数：256  
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内容概要

本书是Springer经典数学教材系列之一。该系列包含已出版的400多本教材，许多已经被奉为经典并该科目的标准参考书。该书对von Neumann代数理论给出了全面而详细的介绍。几乎包含该科目的所有基本结果。对于初学着和专家来说本书都是一本非常难得的参考书。    读者对象：数学专业的研究生和相关专业的科研人员。

书籍目录

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*-Algebras3.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*-AlgebrasBibliographySubject IndexList of Symbols