Author | Megginson, Robert E. author |
---|---|
Title | An Introduction to Banach Space Theory [electronic resource] / by Robert E. Megginson |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0603-3 |
Descript | XIX, 599 p. online resource |
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 Baire 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 Jamesโs Weak Compactness Theorem -- 2.10 Extreme Points -- 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 Jamesโs Space J -- 5 Rotundity and Smoothness -- 5.1 Rotundity -- 5.2 Uniform Rotundity -- 5.3 Generalizations of Uniform Rotundity -- 5.4 Smoothness -- 5.5 Uniform Smoothness -- 5.6 Generalizations of Uniform Smoothness -- A Prerequisites -- B Metric Spaces -- D Ultranets -- References -- List of Symbols