Preface
1 Basic Concepts
1.1 Preliminaries
1.2 Norms
1.3 First Properties of Normed Spaces
1.4 Linear Operators Between Normed Spaces
1.5 Bake Category
1.6 Three Fundamental Theorems
1.7 Quotient Spaces
1.8 Direct Sums
1.9 The Hahn-Banach Extension Theorems
1.10 Dual Spaces
1.11 The Second Dual and Reflexivity
1.12 Separability
1.13 Characterizations of Reflexivity
2 The Weak and Weak Topologies
2.1 Topology and Nets
2.2 Vector Topologies
2.3 Metrizable Vector Topologies
2.4 Topologies Induced by Families of Functions
2.5 The Weak Topology
2.6 The Weak Topology
2.7 The Bounded Weak Topology
2.8 Weak Compactness
2.9 Jamess Weak Compacteness Theorem
2.10 Support Points and Subreflexivity
2.11 Support Points and Subreflexivity
3 Linear Operators
3.1 Adjoint Operators
3.2 Projections and Complemented Subspaces
3.3 Banach Algebras and Spectra
3.4 Compact Operators
3.5 Weakly Compact Operators
4 Schauder Bases
4.1 First Properties of Schauder Bases
4.2 Unconditional Bases
4.3 Equivalent Bases
4.4 Bases and Duality
4.5 Jamess Space J
5 Rotundity and Smoothness
5.1 Rotundity
5.2 Uniform Rotundity
5.3 Generalztions of Uniform Rotundity
5.4 Smoothness
5.5 Unifrom Smoothness
5.6 Generaliztions of Unifrom Smoothness
A Prerequistes
B Metric Spaces
C The Spaces lp and en/p， 1≤p≤∞
D Ultranets
References
List of Symbols
Index
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