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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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PrefaceIntroductionNotation and ConventionsProducts and the Product TopologyFinite-Dimensional Spaces and Rieszs LemmaThe Daniell Integral1.Basic Definitions and Examples1.1 Examples of Banach Spaces1.2 Examples and Calculation of Dual Spaces2.Basic Principles with Applications2.1 The Hahn-BanachTheorem2.2 The Banach-SteinhausTheorem. The Open-Mapping and Closed-Graph Theorems2.4 Applications of the Basic Principles3.Weak Topologies and Applications3.1 Convex Sets and Minkowski Functionals3.2 Dual Systems and Weak Topologies3.3 Convergence and Compactness in Weak Topologies3.4 The Krein-MilmanTheorem4.Operators on Banach Spaces4.1 Preliminary Facts and Linear Projections4.2 Adjoint Operators4.3 Weakly Compact Operators4.4 Compact Operators4.5 The Riesz-Schauder Theory4.6 Strictly Singular and Strictly Cosingular Operators4.7 Reflexivity and Factoring Weakly Compact Operators5.Bases in Banach Spaces5.1 Introductory Concepts5.2 Bases in Some Spe Spaces5.3 Equivalent Bases and Complemented Subspaces5.4 Basic Selection Principles6.Sequences, Series, and a Little Geometry in Banach Spaces6.1 Phillips Lemma6.2 Spe Bases and Reflexivity in Banach Spaces6.3 Unconditionally Converging and Dunford-Pettis Operators6.4 Support Functionals and Convex Sets6.5 Convexity and the Differentiability of NormsBibliographyAuthor/Name IndexSubject IndexSymbol Index编辑后记
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