功能分析：入门课程（2018年版）
This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding of key concepts, while exercises at the end of each chapter provide ample opportunities for practice with the material. Proofs of theorems such as the Uniform Bounded Theory, the Open Mapping Theorem, and the Closed Graph Theorem are worked through step-by-step, providing an accessible avenue to understanding these important results. The prerequisites for this book are linear algebra and elementary real analysis, with two introductory chapters providing an overview of material necessary for the subsequent text. Functional Analysis offers an elementary approach ideal for the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course.
这本书内容简洁，提供了对泛函分析的温和介绍。各章节涵盖了诸如特殊空间、赋范空间、线性泛函和希尔伯特空间等核心主题。许多例子和反例有助于理解关键概念，而每章末的练习则为材料的应用提供了充足的实践机会。书中详细地解释了诸如一致有界定理、开映射定理以及闭图象定理等定理的证明过程，提供了一条易于理解这些重要结果的道路。这本书的要求是线性代数和基本实分析，前两章给出了必要的背景知识概述。《泛函分析》为上本科或初年级研究生的理想入门教材。主要目的是作为一学期的基础课程使用，本书也是独立自学或作为阅读课程基础的完美资源。
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