谱理论简明教程 英文版

本书以作者提供的具备 测度论和基础泛函分析为基 础，为了计算无限维空间中 特殊算子谱，特别是Hilbert 空间中的算子，书中在算子 理论基本问题的内容框架内 讲述了现代分析的基本工具 。工具众多，提供了解决超 越谱计算之外问题的更加具 体方法的基础，这些问题如 量子物理数学基础，非交换 K理论，简单C*代数的分类 。目次：谱理论和Banach 代数；Hilbert空间上的算子 ；渐进：紧扰动和 Fredholm理论；方法和应 用。

Preface Chapter 1.Spectral Theory and Banach Algebras 1.1.Origins of Spectral Theory 1.2.The Spectrum of an Operator 1.3.Banach Algebras: Examples 1.4.The Regular Representation 1.5.The General Linear Group of A 1.6.Spectrum of an Element of a Banach Algebra 1.7.Spectral Radius 1.8.Ideals and Quotients 1.9.Commutative Banach Algebras 1.10.Examples: C(X) and the Wiener Algebra 1.11.Spectral Permanence Theorem 1.12.Brief on the Analytic Functional Calculus Chapter 2.Operators on Hilbert Space 2.1.Operators and Their C*-Algebras 2.2.Commutative C*-Algebras 2.3.Continuous Functions of Normal Operators 2.4.The Spectral Theorem and Diagonalization 2.5.Representations of Banach *-Algebras 2.6.Borel Functions of Normal Operators 2.7.Spectral Measures 2.8.Compact Operators 2.9.Adjoining a Unit to a C*-Algebra 2.10.Quotients of C*-Algebras Chapter 3.Asymptotics: Compact Perturbations and Fredholm Theory 3.1.The Calkin Algebra 3.2.Riesz Theory of Compact Operators 3.3.Fredholm Operators 3.4.The Fredholm Index Chapter 4.Methods and Applications 4.1.Maximal Abelian yon Neumann Algebras 4.2.Toeplitz Matrices and Toeplitz Operators 4.3.The Toeplitz C*-Algebra 4.4.Index Theorem for Continuous Symbols 4.5.Some H2 Function Theory 4.6.Spectra of Toeplitz Operators with Continuous Symbol 4.7.States and the GNS Construction 4.8.Existence of States: The Gelfand-Naimark Theorem Bibliography Index