算子代数理论 Theory of Operator Algebras 日 竹崎政路 Takesa-ki M. 扫描版[DJVU]

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资源信息： 中文名: 算子代数理论 原名: Theory of Operator Algebras 作者: (日)竹崎政路(Takesa-ki,M.) 资源格式: DJVU 版本: 扫描版 出版社: Springer 书号: 354042248X 发行时间: 2001年 地区: 美国 语言: 英文 概述:

内容简介: 算子代数是20世纪最伟大的数学家之一，计算机之父John von Neumann于1929年首创的。他的“算子环”后来为纪念他称为冯·诺伊曼代数。所谓算子代数实际上是冯·诺伊曼代数和C*代数的统称。到20世纪70年代，算子代数还只是泛函分析的一个分支，由于法国数学家A.Connes的工作，算子代数成为与许多数学和物理分支密切相关的核心领域，他还创立了“非交换几何学”这个前沿领域。 本书作者是算子代数领域权威学者。 本书为该领域最完全、最现代的参考书之一，是从事该领域研究工作的必备作。 内容截图:

目录: Vol-I Introduction. Chapter Ⅰ Fundamentals of Banach Algebras and C*-Algebras 0. Introduction 1. Banach Algebras 2. Spectrum and Functional Calculu 3. Gelfand Representation of Abelian Banach Algebras 4. Spectrum and Functional Calculus in C*-Algebra 5. Continuity of Homomorphisms 6. Positive Cones of C*-Algebras 7. Approximate Identities in C*-Algebras 8. Quotient Algebras of C*-Algebras 9. Representations and Positive Linear Functionals 10. Extreme Points of the Unit Ball of a C*-Algebra 11. Finite Dimensional C*-Algebras Notes Exercises ChapterⅡ Topologies and Density Theorems in Operator Algebras 0. Introduction 1. Banach Spaces of Operators on a Hilbert Space 2. Locally Convex Topologies in L 3. The Double Commutation Theorem of J. von Neumann 4. Density Theorems Notes Chapter Ⅲ Conjugate Spaces 0. Introduction 1. Abelian Operator Algebras 2. The Universal Enveloping von Neumann Algebra of a C*-Algebra 3. W*-Algebras 4. The Polar Decomposition and the Absolute Value of Functionals 5. Topological Properties of the Conjugate Space 6. Semicontinuity in the Universal Enveloping von Neumann Algebra* Notes.. Chapter Ⅳ Tensor Products of Operator Algebras and Direct Integrals 0. Introduction 1. Tensor Product of Hilbert Spaces and Operators 2. Tensor Products of Banach Spaces 3. Completely Positive Maps 4. Tensor Products of C*-Algebras 5. Tensor Products of W*-Algebras Notes 6. Integral Representations of States 7. Representation of L2(Γ，μ) (0+) , L(Γ，μ) (0+)γ M*， and L(Γ，μ)(0+) M 8. Direct Integral of Hilbert Spaces,Representations, and von NeumannAlgebras Notes Chapter Ⅴ Type, s of von Neumann Algebras and Traces 0. Introduction 1. Projections and Types of von Neumann Algebras 2. Traces on von Neumann Algebras Notes 3. Multiplicity of a yon Neumann Algebra on a Hilbert Space 4. Ergodic Type Theorem for von Neumann Algebras* 5. Normality of Separable Representations* 6. The Borel Spaces of von Neumann Algebras 7. Construction of Factors of Type II and Type III Notes Appendix Polish Spaces and Standard Borel Spaces Bibliography Monographs Papers Notation Index Subject Index Vol-II Vol-III