巴拿赫空间理论讲义（英文影印版） 出版时间：2012年版 内容简介 《巴拿赫空间理论讲义(影印版)》是一部讲述巴纳赫空间的教程。书中提供了全面了解现代巴纳赫空间理论的观点和技巧，重点强调典型勒贝格空间Lp和连续函数空间；同时也强调了巴纳赫空间同构理论，基和基本序列的应用技巧。这些都旨在为读者提供必需的技巧工具，无需了解许多更多的概念而直达学术前沿。 目录 1 Bases and Basic Sequences 1.1.Schauder bases 1.2 Examples: Fourier series 1.3 Equivalence of bases and basic sequences 1.4 Bases and basic sequences: discussion 1.5 Constructing basic sequences 1.6 The Eberlein-Smulian Theorem Problems The Classical Sequence Spaces 2.1 The isomorphic structure of the lp-spaces and co 2.2 Complemented subspaces of lp (1 < p <∞) and co 2.3 The space l1 2.4 Convergence of series 2.5 Complementability of c0 Problems Special Types of Bases 3.1 Unconditional bases 3.2 Boundedly-complete and shrinking bases 3.3 Nonreflexive spaces with unconditional bases 3.4 The James space J 3.5 A litmus test for unconditional bases Problems 4 Banach Spaces of Continuous Functions 4.1 Basic properties 4.2 A characterization of real C(K)-spaces 4.3 Isometrically injective spaces 4.4 Spaces of continuous functions on uncountable compact metric spaces 4.5 Spaces of continuous functions on countable compact metric spaces Problems 5 L1(μ)-Spaces and C(K)-Spaces 5.1 General remarks about L1(μ)-spaces 5.2 Weakly compact subsets of L1 (μ) 5.3 Weak compactness in M(K) 5.4 The Dunford-Pettis property 5.5 Weakly compact operators on C(K)-spaces 5.6 Subspaces of L1(μ)-spaces and C(K)-spaces Problems 6 The Lp-Spaces for 1 < p <∞ 6.1 Conditional expectations and the Haar basis 6.2 Averaging in Banach spaces …… 7 Factorization Theory 8 Absolutely Summing Operators Perfectly Homogeneous Bases and Their Applications 10 lp-Subspaces of Banach Spaces 11 Finite Representability of lp-Spaces 12 An Introduction to Local Theory 13 Important Examples of Banach Spaces A Fundamental Notions B Elementary Hilbert Space Theory C Main Features of Finite-Dimensional Spaces D Cornerstone Theorems of Functional Analysis D.1 The Hahn-Banach Theorem D.2 Baire's Theorem and its consequences E Convex Sets and Extreme Points F The Weak Topologies G Weak Compactness of Sets and Operators List of Symbols References Index
