譜理論簡明教程(英文)

譜理論簡明教程(英文)
定價：150 元
NT $ 131
 

內容簡介

以作者提供的具備測度論和基礎泛函分析的一二年級研究生十五周課程為基礎，為了計算無限維空間中特殊算子譜，特別是Hilbert空間中的算子，書中在算子理論基本問題的內容框架內講述了現代分析的基本工具。工具眾多，提供了解決超越譜計算之外問題的更加具體方法的基礎，這些問題如量子物理數學基礎，非交換K理論，簡單C*代數的分類。目次：譜理論和Banach代數；Hilbert空間上的算子；漸進：緊擾動和Fredholm理論；方法和應用。
 

目錄

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
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