Banach Space Theory: The Basis for Linear and Nonlinear Analysis

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Springer Science & Business Media, Feb 4, 2011 - Mathematics - 822 pages
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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.
  

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Contents

2 HahnBanach and Banach Open Mapping Theorems
53
3 Weak Topologies and Banach Spaces
83
4 Schauder Bases
179
5 Structure of Banach Spaces
237
6 FiniteDimensional Spaces
291
7 Optimization
331
8 C1Smoothness in Separable Spaces
383
9 Superreflexive Spaces
429
13 Weakly Compactly Generated Spaces
575
14 Topics in Weak Topologies on Banach Spaces
617
15 Compact Operators on Banach Spaces
657
16 Tensor Products
687
17 Appendix
733
References
751
Symbol Index
777
Subject Index
781

10 Higher Order Smoothness
464
11 Dentability and Differentiability
479
12 Basics in Nonlinear Geometric Analysis
521

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All of the authors have previously published with Springer.

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