●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． itive 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． itive 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．Voiculescu's 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

算子理論在現代數學的許多重要領城諸如泛函分析、微分方程、指標論、表示論、數學物理中充當重要角色。本書覆蓋了算子理論的中心課題，敘述清晰簡潔，讀者很容易與Conway的寫作產生互動。本書前幾章介紹和回顧了C*-代數、正規算子、緊算子和非正規算子，主題包含譜理論、泛函演算和Fredholm指標。此外，還論述了算子理論和解析函數之間某些深刻的聯繫。後續章節講述了更高級的主題，包括C*-代數的表示、緊微擾和vonNeumann代數等。重要結果覆蓋了諸如Sz.-Nagy伸縮定理、Weyl-vonNeumann-Berg定理和vonNeumann代數的分類，同樣也講述了對Fredholm理論的處理，這些高級論題均處於當今研究的中心。最後一章介紹了自返子空間，即由其不變子空間決定的算子子空間。這些連同超自返空間是現代非對稱代數研究中成功的插曲之一。Conway教授的處理使本書成為一本引人入勝但又相當縝密等