泛函分析导引（影印版）

本书快速但精确细致地 介绍了泛函分析，除基础研 究生分析教材中的基本内容 外，还包括更复杂的主题， 如谱理论、凸性和不动点定 理。本书的一个特点是包含 了大量的例题甚至一些应用 。全书最后陈述并证明了 Lomonosov关于不变子空间 的激动人心的结果。

Preface 1 Fundamentals 1.1 What is Functional Analysis 1.2 Normed Linear Spaces 1.3 Finite-Dimensional Spaces 1.4 Linear Operators 1.5 The Baire Category Theorem 1.6 The Three Big Results 1.7 Applications of the Big Three 2 Ode to the Dual Space 2.1 Introduction 2.2 Consequences of the Hahn-Banach Theorem 3 Hilbert Space 3.1 Introduction 3.2 The Geometry of Hilbert Space 4 The Algebra of Operators 4.1 Preliminaries 4.2 The Algebra of Bounded Linear Operators 4.3 Compact Operators 5 Banach Algebra Basics 5.1 Introduction to Banach Algebras 5.2 The Structure of a Banach Algebra 5.3 Ideals 5.4 The Wiener Tauberian Theorem 6 Topological Vector Spaces 6.1 Basic Ideas 6.2 Fréchet Spaces 7 Distributions 7.1 Preliminary Remarks 7.2 What is a Distribution 7.3 Operations on Distributions 7.4 Approximation of Distributions 7.5 The Fourier Transform 8 Spectral Theory 8.1 Background 8.2 The Main Result 9 Convexity 9.1 Introductory Thoughts 9.2 Separation Theorems 9.3 The Main Result 10 Fixed-Point Theorems 10.1 Banach's Theorem 10.2 Two Applications 10.3 The Schauder Theorem Table of Notation Glossary Bibliography Index About the Author