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醉染图书算子理论教程9787040469158
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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-sr oology
21.Inflation and the topologies
Chapter 4.Some Non-Normal Operators
22.Algebras and lattices
.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.sicentral 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 an daty
60.Hypereflexive von Neumann algebras
61.Some examples of operators
Bibliography
Index
List of Symbols
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