Sequences and Series in Banach Spaces

✍ Scribed by Joseph Diestel (auth.)

• Publisher: Springer New York
• Year: 1984
• Tongue: English
• Leaves: 272
• Series: Graduate Texts in Mathematics 92
• Category: Library

✦ Table of Contents

Content:
Front Matter....Pages iii-xii
Riesz’s Lemma and Compactness in Banach Spaces....Pages 1-8
The Weak and Weak* Topologies: An Introduction....Pages 9-16
The Eberlein-� mulian Theorem....Pages 17-23
The Orlicz-Pettis Theorem....Pages 24-31
Basic Sequences....Pages 32-57
The Dvoretsky-Rogers Theorem....Pages 58-65
The Classical Banach Spaces....Pages 66-123
Weak Convergence and Unconditionally Convergent Series in Uniformly Convex Spaces....Pages 124-146
Extremal Tests for Weak Convergence of Sequences and Series....Pages 147-172
Grothendieck’s Inequality and the Grothendieck-Lindenstrauss-Pelczynski Cycle of Ideas....Pages 173-191
An Intermission: Ramsey’s Theorem....Pages 192-199
Rosenthal’s l 1 Theorem....Pages 200-218
The Josefson-Nissenzweig Theorem....Pages 219-225
Banach Spaces with Weak Sequentially Compact Dual Balls....Pages 226-240
The Elton-Odell (1 + ε)-Separation Theorem....Pages 241-255
Back Matter....Pages 257-263