线性泛函分析
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内容提要：
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。 目录：
1 Preliminaries
1.1 Linear Algebra 1.2 Metric Spaces 1.3 Lebesgue Integration 2 Normed Spaces 2.1 Examples of Normed Spaces 2.2 Finite-dimensional Normed Spaces 2.3 Banach Spaces 3 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 series 4 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 Operators 5 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 Operators 7 Integral and Differential Equations 8 Solutions to Exercises Furthe Reading References Notation Index Index 前言：
This book provides an introduction to the ideas and methods of linear functional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the theory of metric spaces). .
Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equations. Often, the appropriate setting turned out to be a vec..
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