Normed Linear Spaces (ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge)

Foreword to the First Edition Foreword to the Third Edition Contents Chapter I. Linear Spaces § 1. Linear Spaces and Linear Dependence § 2. Linear Functions and Conjugate Spaces § 3. The Hahn-Banach Extension Theorem § 4. Linear Topological Spaces § 5. Conjugate Spaces § 6. Cones, Wedges, Order Relations Chapter II. Normed Linear Spaces § 1. Elementary Definitions and Properties § 2. Examples of Normed Spaces; Constructions of New Spaces from Old § 3. Category Proofs § 4. Geometry and Approximation § 5. Comparison of Topologies in a Normed Space Chapter III. Completeness, Compactness, and Reflexivity § 1. Completeness in a Linear Topological Space § 2. Compactness § 3. Completely Continuous Linear Operators § 4. Reflexivity § 5. Weak Compactness and Structure in Normed Spaces Chapter IV. Unconditional Convergence and Bases § 1. Series and Unconditional Convergence § 2. Tensor Products of Locally Convex Spaces § 3. Schauder Bases in Separable Spaces § 4. Unconditional Bases Chapter V. Compact Convex Sets and Continuous Function Spaces § 1. Extreme Points of Compact Convex Sets § 2. Fixed-point Theorems § 3. Some Properties of Continuous Function Spaces § 4. Characterizations of Continuous Function Spaces among Banach Spaces Chapter VI. Norm and Order § 1. Vector Lattices and Normed Lattices § 2. Linear Sublattices of Continuous Function Spaces § 3. Monotone Projections and Extensions § 4. Special Properties of (AL)-Spaces Chapter VII. Metric Geometry in Normecl Spaces § 1. Isometry and the Linear Structure § 2. Rotundity and Smoothness § 3. Characterizations of Inner-Product Spaces § 4. Isomorphisms to Improve the Norm A. Rotundity, smoothness, and convex functions B. Superreflexive spaces Chapter VIII. Reader's Guide A: To 1956 B: To 1972 Bibliography A・B C D E・F・G H J・K L・M N・O・P R S T・U・V・W・Y・Z Index of Citations Index of Symbols ConstantsJrom Set Theory and Logic Non-alphabetical Symbols Jor Mathematical Operations Symbols which are Names or Abbreviations of Names Symbols used as Labels for Properties or Conditions Subject Index