Methods in Banach Space Theory

by Edited by Jesus M. F. Castillo , William B. Johnson

• ISBN13: 9780521685689
• ISBN10: 0521685680
• Format: Paperback
• Copyright: 2006-12-11
• Publisher: Cambridge University Press

Summary

This book presents an overview of modern Banach space theory. It contains sixteen papers that reflect the wide expanse of the subject. Articles are gathered into five sections according to methodology rather than the topics considered. The sections are: geometrical methods; homological methods; topological methods; operator theoretic methods; and also function space methods. Each section contains survey and research papers describing the state-of-the-art in the topic considered as well as some of the latest most important results. Researchers working in Banach space theory, functional analysis or operator theory will find much of interest here.

Table of Contents

Table of Contents	v
Preface	vii
Acknowledgements	ix
Picture: closing at the main lecture room	xi
1. GEOMETRICAL METHODS
Saturated extensions, the attractors method and Hereditarily James Tree Spaces	1
by Spiros A. Argyros, Alexander D. Arvanitakis and Andreas G. Tolias
The Daugavet property for Lindenstrauss spaces	91
by J. Becerra and M. Martin
Weakly null sequences in the Banach space C(K)	97
by I. Gasparis, E. Odell and B. Wahl
2. HOMOLOGICAL METHODS
Yet another proof of Sobczyk's theorem	133
by Félix Cabello Sánchez
The category of exact sequences of Banach spaces	139
by Jesús M.F. Castillo and Yolanda Moreno
Extension problems for C(K) spaces and twisted sums	159
by N.J. Kalton
Palamodov's questions from Homological methods in the theory of locally convex spaces	169
by Jochen Wengenroth
3. TOPOLOGICAL METHODS
Ordinal representability in Banach spaces	183
by M.J. Campión, J.C. Candeal, A.S. Granero and E. Induráin
Overclasses of the class of Radon-Nikodým compact spaces	197
by Marián Fabian
Convexity, compactness and distances	215
by A.S. Granero and Marcos Sánchez
4. OPERATOR THEORY METHODS
Weyl's and Browder's theorems through the quasi-nilpotent part of an operator	239
by Pietro Aiena and Maria Teresa Biondi
Multiplications and elementary operators in the Banach space setting	253
by Eero Saksman and Hans-Olav Tylli
Interpolation of Banach Spaces by the γ-method	293
by Jesús Suárez and Lutz Weis
5. FUNCTION SPACE METHODS
Solvability of an integral equation in BC(R+)	307
by J. Caballero, B. López and K. Sadarangani
Harald Bohr meets Stefan Banach	317
by Andreas Defant and Christopher Prengel
Selected problems on the structure of complemented subspaces of Banach spaces	341
by Aleksander Pelczynski
List of participants	355
Picture: some like it fun.	358