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| 內容簡介： |
本书主要包括巴拿赫空 间的基本定义和举例、巴拿 赫空间应用的基本原则、弱 拓扑及其应用、巴拿赫空间 中的算子、共轭算子、巴拿 赫空间的基础、一些特殊空 间的基础、基本挑选原则、 巴拿赫空间中的序列和几何 学、 斯引理等内容。
希望读者通过研究本书中介 绍的思想和技巧，遵循本书 介绍的许多结果所指示的方 向，帮助读者对巴拿赫大部 分的工作和遗产所蕴含的美 丽和微妙之处有 深入的了 解，也希望本书可以令读者 对这种丰富的数学领域产生 赞赏和理解之情。本书适合 于对巴拿赫空间感兴趣的学 者或数学爱好者参考阅读。
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| 目錄：
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Preface
Introduction
Notation and Conventions
Products and the Product Topology
Finite-Dimensional Spaces and Riesz''s Lemma
The Daniell Integral
1.Basic Definitions and Examples
1.1 Examples of Banach Spaces
1.2 Examples and Calculation of Dual Spaces
2.Basic Principles with Applications
2.1 The Hahn-BanachTheorem
2.2 The Banach-SteinhausTheorem
2.3 The Open-Mapping and Closed-Graph Theorems
2.4 Applications of the Basic Principles
3.Weak Topologies and Applications
3.1 Convex Sets and Minkowski Functionals
3.2 Dual Systems and Weak Topologies
3.3 Convergence and Compactness in Weak Topologies
3.4 The Krein-MilmanTheorem
4.Operators on Banach Spaces
4.1 Preliminary Facts and Linear Projections
4.2 Adjoint Operators
4.3 Weakly Compact Operators
4.4 Compact Operators
4.5 The Riesz-Schauder Theory
4.6 Strictly Singular and Strictly Cosingular Operators
4.7 Reflexivity and Factoring Weakly Compact Operators
5.Bases in Banach Spaces
5.1 Introductory Concepts
5.2 Bases in Some Special Spaces
5.3 Equivalent Bases and Complemented Subspaces
5.4 Basic Selection Principles
6.Sequences, Series, and a Little Geometry in Banach Spaces
6.1 Phillips'' Lemma
6.2 Special Bases and Reflexivity in Banach Spaces
6.3 Unconditionally Converging and Dunford-Pettis Operators
6.4 Support Functionals and Convex Sets
6.5 Convexity and the Differentiability of Norms
Bibliography
AuthorName Index
Subject Index
Symbol Index
编辑后记
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