算子理论教程
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作者(美)约翰·康韦
出版社高等教育出版社
ISBN9787040469158
出版时间2018-06
装帧精装
开本16开
定价169元
货号1201705056
上书时间2024-11-05
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目录
Chapter 1．Introduction to C*-Algebras
1．Definition and examples
2．Abelian C*-algebras and the Functional Calculus
3．The positive elements in a C*-algebra
4．Approximate identities
5．Ideals in a C*-algebra
6．Representations of a C*-algebra
7．Positive linear functionals and the GNS construction
Chapter 2．Normal Operators
8．Some topologies on B（H）
9．Spectral measures
10．The Spectral Theorem
11．Star-cyclic normal operators
12．The commutant
13．Von Neumann algebras
14．Abelian von Neumann algebras
15．The functional calculus for normal operators
Chapter 3．Compact Operators
16．C*-algebras of compact operators
17．Ideals of operators
18．Trace class and Hilbert-Schmidt operators
19．The dual spaces of the compact operators and the trace class
20．The weak-star topology
21．Inflation and the topologies
Chapter 4．Some Non-Normal Operators
22．Algebras and lattices
23．Isometries
24．Unilateral and bilateral shifts
25．Some results on Hardy spaces
26．The functional calculus for the unilateral shift
27．Weighted shifts
28．The Volterra operator
29．Bergman operators
30．Subnormal operators
31．Essentially normal operators
Chapter 5．More on C*-Algebras
32．Irreducible representations
33．Positive maps
34．Completely positive maps
35．An application： Spectral sets and the Sz．-Nagy DilationTheorem
36．Quasicentral approximate identitites
Chapter 6．Compact Perturbations
37．Behavior of the spectrum under a compact perturbation
38．Bp perturbations of hermitian operators
39．The Weyl-von Neumann-Berg Theorem
40．Voiculescus Theorem
41．Approximately equivalent representations
42．Some applications
Chapter 7．Introduction to Von Neumann Algebras
43．Elementary properties and examples
44．The Kaplansky Density Theorem
45．The Pedersen Up-Down Theorem
46．Normal homomorphisms and ideals
47．Equivalence of projections
48．Classification of projections
49．Properties of projections
50．The structure of Type I algebras
51．The classification of Type I algebras
52．Operator-valued measurable functions
53．Some structure theory for continuous algebras
54．Weak-star continuous linear functionals revisited
55．The center-valued trace
Chapter 8．Reflexivity
56．Fundamentals and examples
57．Reflexive operators on finite dimensional spaces
58．Hyperreflexive subspaces
59．Reflexivity and duality
60．Hypereflexive von Neumann algebras
61．Some examples of operators
Bibliography
Index
List of Symbols
内容摘要
算子理论在现代数学的许多重要领城诸如泛函分析、微分方程、指标论、表示论、数学物理中充当重要角色。本书覆盖了算子理论的中心课题，叙述清晰简洁，读者很容易与Conway的写作产生互动。本书前几章介绍和回顾了C*-代数、正规算子、紧算子和非正规算子，主题包含谱理论、泛函演算和Fredholm指标。此外，还论述了算子理论和解析函数之间某些深刻的联系。后续章节讲述了更不错的主题，包括C*-代数的表示、紧微扰和vonNeumann代数等。重要结果覆盖了诸如Sz.-Nagy伸缩定理、Weyl-vonNeumann-Berg定理和vonNeumann代数的分类，同样也讲述了对Fredholm理论的处理，这些不错论题均处于当今研究的中心。很后一章介绍了自返子空间，即由其不变子空间决定的算子子空间。这些连同超自返空间是现代非对称代数研究中成功的插曲之一。Conway教授的处理使本书成为一本引人入胜但又相当缜密的教材，适合于已经上过泛函分析标准课程的研究生。
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