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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.…mehr
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.
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Autorenporträt
Jesús M. F. Castillo is a Professor in the Department of Mathematics at Universidad de Extremadura. William B. Johnson is a Distinguished Professor of Mathematics and holds the A.G. M.E. Chair of Mathematics at Texas AM University.
Inhaltsangabe
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 Sobczyk's 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. Palamodov's 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. Weyl's and Browder's 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.
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 Sobczyk's 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. Palamodov's 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. Weyl's and Browder's 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.
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