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醉染图书算子理论教程9787040469158
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Chapter 1.Introduction to C*-Algebras1.Definition and examples2.Abelian C*-algebras and the Functional Calculus3.The positive elements in a C*-algebra4.Approximate identities5.Ideals in a C*-algebra6.Representations of a C*-algebra7.Positive linear functionals and the GNS constructionChapter 2.Normal Operators8.Some topologies on B(H)9.Spectral measures10.The Spectral Theorem11.Star-cyclic normal operators12.The commutant13.Von Neumann algebras14.Abelian von Neumann algebras15.The functional calculus for normal operatorsChapter 3.Compact Operators16.C*-algebras of compact operators17.Ideals of operators18.Trace class and Hilbert-Schmidt operators19.The dual spaces of the compact operators and the trace class20.The weak-sr oology21.Inflation and the topologiesChapter 4.Some Non-Normal Operators22.Algebras and lattices.Isometries24.Unilateral and bilateral shifts25.Some results on Hardy spaces26.The functional calculus for the unilateral shift27.Weighted shifts28.The Volterra operator29.Bergman operators30.Subnormal operators31.Essentially normal operatorsChapter 5.More on C*-Algebras32.Irreducible representations33.Positive maps34.Completely positive maps35.An application: Spectral sets and the Sz.-Nagy DilationTheorem36.sicentral approximate identititesChapter 6.Compact Perturbations37.Behavior of the spectrum under a compact perturbation38.Bp perturbations of hermitian operators39.The Weyl-von Neumann-Berg Theorem40.Voiculescus Theorem41.Approximately equivalent representations42.Some applicationsChapter 7.Introduction to Von Neumann Algebras43.Elementary properties and examples44.The Kaplansky Density Theorem45.The Pedersen Up-Down Theorem46.Normal homomorphisms and ideals47.Equivalence of projections48.Classification of projections49.Properties of projections50.The structure of Type I algebras51.The classification of Type I algebras52.Operator-valued measurable functions53.Some structure theory for continuous algebras54.Weak-star continuous linear functionals revisited55.The center-valued traceChapter 8.Reflexivity56.Fundamentals and examples57.Reflexive operators on finite dimensional spaces58.Hyperreflexive subspaces59.Reflexivity an daty60.Hypereflexive von Neumann algebras61.Some examples of operatorsBibliographyIndexList of Symbols
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