Sequences and Series in Banach Spaces

✍ Scribed by Joseph Diestel

• Publisher: Springer
• Year: 1984
• Tongue: English
• Leaves: 269
• Category: Library

✦ Table of Contents

Title page
Preface
Some Standard Notations and Conventions
Contents (detailed but unpaginated)
I. Riesz's Lemma and Compactness in Banach Spaces
II. The Weak and Weak Topologies: an Introduction
III. The Eberlein-Smulian Theorem
IV. The Orlicz-Pettis Theorem
V. Basic Sequences
VI. The Dvoretsky-Rogers Theorem
VII. The Classical Banach Spaces
VIII. Weak Convergence and Unconditionally Convergent Series in Uniformly Convex Spaces
IX. Extremal Tests for Weak Convergence of Sequences and Series
X. Grothendieck's Inequality and the Grothendieck-Lindenstrauss-Pelczynski Cycle of Ideas
An Intermission: Ramsey's theorem
XI. Rosenthal's l₁-theorem
XII. The Josefson-Nissenzweig Theorem
XIII. Banach Spaces with Weak-Sequentially Compact Dual Balls
XIV. The Elton-Odell (1+ε)-Separation Theorem
Index