The James forest / Helga Fetter, Berta Gamboa de Buen.

Format:

Book

Author/Creator:

Fetter, Helga, 1944- author.

Gamboa de Buen, Berta, 1954- author.

Series:

London Mathematical Society lecture note series ; 236.

London Mathematical Society lecture note series ; 236

Language:

English

Subjects (All):

Banach spaces.

Physical Description:

1 online resource (xi, 255 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1997.

Language Note:

English

Summary:

The James space J and the James tree space JT were constructed as counterexamples to several outstanding conjectures in Banach space theory. This book is a compendium of most of the known results about these spaces, frequently taken from the original sources, but presented in a unified and up to date fashion. Generalisations of J and JT are also discussed and other pathological Banach spaces are introduced. Specialists will welcome this book for its drawing together of classical material and recent results. Graduate students should also find that this book offers an excellent introduction to more advanced topics in Banach space theory.

Contents:

Cover; Title; Copyright; Dedication; Contents; Foreword; Prologue; Preface; Chapter 1. Preliminaries; Chapter 2. The James space J; 2.a Definition and fundamental properties of J; 2.b Finite representability; 2.c Complemented subspaces of J and the space J; 2.d Basic sequences and the primarity of J; 2.e Isometries of the space J; 2.f J as a conjugate space; 2.g The dual of the James space; 2.h The Banach-Saks properties and the spreading models of J and J*; 2.i J* has cotype 2; 2.j Appendix: πλ -spaces, bounded approximation property and finite dimensional decompositions

2.k Appendix: Lipα([0,1],X) and Lp(X)(i) An isomorphism between lα(x) and Lipα([0,1],X); (ii) About the space Lp(X) of Bochner integrable functions; Chapter 3. The James tree space JT; 3.a The space JT; 3.b The fixed point property; 3.c The conjugates of JT; 3.d The norms of JT and JT* have the Kadec-Klee property; Chapter 4. What else is there about J and JT?; 4.a More about J; 4.b More about JT; 4.c Generalizations of J; 4.d Generalizations of JT; Chapter 5. Other pathological spaces; (i) Schreier's space S.; (ii) James uniformly non-octahedral space.; (iii) Baernstein's space B.

(iv) Tsirelson's space.(vi) Gowers-Maurey space.; References; Index of citations; List of Special Symbols; Subject Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and indexes.

ISBN:

1-139-88529-4

1-107-36743-3

1-107-37200-3

1-107-36252-0

1-107-36944-4

1-299-40506-1

1-107-36497-3

0-511-66237-8