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醉染图书泛函分析——巴拿赫空间理论入门9787560389448
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新春将至,本公司假期时间为:2025年1月23日至2025年2月7日。2月8日订单陆续发货,期间带来不便,敬请谅解!
Preface
Introduction
Notation and Conventions
Products and the Product Topology
Finite-Dimensional Spaces and Rieszs 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
. 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 Spe 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 Spe 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
Author/Name Index
Subject Index
Symbol Index
编辑后记
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