线性泛函分析

1 Preliminaries 1.1 Linear Algebra 1.2 Metric Spaces 1.3 Lebesgue Integration2 Normed Spaces 2.1 Examples of Normed Spaces 2.2 Finite-dimensional Normed Spaces 2.3 Banach Spaces3 Inner Product Spaces.Hibert Spaces 3.1 Inner Products 3.2 Orthogonality 3.3 Orthogonal Complements 3.4 Orthonormal Bases in Infiniate Dimensions 3.5 Fourier series4 Linear Operators

1 Preliminaries 1.1 Linear Algebra 1.2 Metric Spaces 1.3 Lebesgue Integration2 Normed Spaces 2.1 Examples of Normed Spaces 2.2 Finite-dimensional Normed Spaces 2.3 Banach Spaces3 Inner Product Spaces.Hibert Spaces 3.1 Inner Products 3.2 Orthogonality 3.3 Orthogonal Complements 3.4 Orthonormal Bases in Infiniate Dimensions 3.5 Fourier series4 Linear Operators 4.1 Continuous Linear Transformaations 4.2 The Norm of a Bounded Linear Operator 4.3 The Space and Dual Spaces 4.4 Inverses of Operators5 Linear Operators on Hilbert Spaces 5.1 The Adjoint of an Operator 5.2 Normal Self-adjoint and Unitary Operators 5.3 The Spectrum of an Operator ……6 Compact Operators7 Integral and Differential Equations8 Solutions to ExercisesFurthe ReadingReferencesNotation IndexIndex

本书以较小的篇幅介绍了线性泛函分析的基本内容：赋范空间和Banach空间，内积空间和Hilbert空间，线性算子，紧算子及其在积分方程和微分方程中的应用。本书内容深入浅出、通俗易懂，重要的概念和定理均有背景介绍，并配有简单例子加以解释；排版层次分明、结构清晰；书的末尾配有习题解答。 本书适合大学高年级学生以及研究生自学或作为教材使用。