Methods in Banach Space Theory

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.

Spis treści:
Acknowledgements
Foreword
Part I. Geometrical Methods
1. Saturated extensions, the attractors method and hereditarily James tree spaces Spiros A. Agyros, Alexander D. Arvanitakis and Andreas G. Tolias
2. The Daugavet property for Lindenstrauss spaces J. Becerra and M. Martín
3. Weakly null sequences in the Banach space I. Gasparis, E. Odell and B. Wahl
Part II. Homological Methods
4. Yet another proof of Sobczyks theorem Félix Cabello Sanchez
5. The category of exact sequences of Banach spaces Jesús M. F. Castillo and Yolanda Moreno
6. Extension problems for C(K)spaces and twisted sums N. J. Kalton
7. Palamodovs questions from homological methods in the theory of locally convex spaces Jochen Wengenroth
Part III. Topological Methods
8. Ordinal representability in Banach spaces M. J. Campión, J. C. Candeal, A. S. Granero and E. Indurain
9. Overclasses of the class of Radon-Nikodym compact spaces Marián Fabian
10. Convexity, compactness and distances A. S. Granero and Marcos Sánchez
Part IV. Operator Theory Methods
11. Weyls and Browders theorems through the quasi-nilpotent part of an operator Pietro Aiena and Maria Teresa Biondi
12. Multiplications and elementary operators in the Banach space setting Eero Saksman and Hans-Olav Tylli
13. Interpolation of Banach spaces by the ?-method Jesús Suárez and Lutz Weis
Part V. Function Space Methods
14. Solvability of an integral equation in BC(R+) J. Caballero, B. López and K. Sadarangani
15. Harold Bohr meets Stefan Banach Andreas Defant and Christopher Prengel
16. Selected problems on the structure of complemented subspaces of Banach spaces Aleksander Pelczynski
List of participants.