中文名: 算子代數理論
原名: Theory of Operator Algebras
作者: (日)竹崎政路(Takesa-ki,M.)
資源格式: DJVU
版本: 掃描版
出版社: Springer
書號: 354042248X
發行時間: 2001年
地區: 美國
語言: 英文
簡介:

內容簡介:
算子代數是20世紀最偉大的數學家之一，計算機之父John von Neumann於1929年首創的。他的“算子環”後來為紀念他稱為馮·諾伊曼代數。所謂算子代數實際上是馮·諾伊曼代數和C*代數的統稱。到20世紀70年代，算子代數還只是泛函分析的一個分支，由於法國數學家A.Connes的工作，算子代數成為與許多數學和物理分支密切相關的核心領域，他還創立了“非交換幾何學”這個前沿領域。
本書作者是算子代數領域權威學者。
本書為該領域最完全、最現代的參考書之一，是從事該領域研究工作的必備作。
內容截圖:

目錄:
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