Normed Linear Spaces

✍ Scribed by Maiilon M. Day

• Publisher: Springer
• Year: 1973
• Tongue: English
• Leaves: 217
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete 21
• Edition: 3
• Category: Library

✦ Table of Contents

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