| Description |
xiii, 820 pages : illustrations ; 24 cm. |
| Series |
CMS books in mathematics,
1613-5237
|
|
CMS books in mathematics.
|
| Bibliography |
Includes bibliographical references (pages 751-775) and indexes. |
| Summary |
Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L₁ theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice. The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book. |
| Contents |
Basic concepts in Banach spaces -- Hahn-Banach and Banach open mapping theorems -- Weak topologies and Banach spaces -- Schauder bases -- Structure of Banach spaces -- Finite-dimensional spaces -- Optimization -- C¹-smoothness in separable spaces -- Superreflexive spaces -- Higher order smoothness -- Dentability and differentiability -- Basics in nonlinear geometric analysis -- Weakly compactly generated spaces -- Topics in weak topologies on Banach spaces -- Compact operators on Banach spaces -- Tensor products -- Appendix: Basics in topology -- Nets and filters -- Nets and filters in topological spaces -- Ultraproducts -- The order topology on the ordinals -- Continuity of set-valued mappings -- The cantor space -- Baire's great theorem -- Polish spaces -- Uniform spaces -- Nets and filters in uniform spaces -- Partitions of unity -- Measure and integral -- Continued fractions and the representation of the irrational numbers. |
| Subject |
Banach spaces.
|
|
Banach spaces. |
| Added Author |
Fabian, Marián J.
|
| ISBN |
9781441975140 hardback |
|
1441975144 hardback |
|
