巴拿赫空间理论讲义（英文影印版）

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

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