C*代数和W*代数
2009-6
世界图书出版公司
章一郎堺
256
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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。
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
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