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＜電子ブック＞
Banach Space Theory : The Basis for Linear and Nonlinear Analysis / by Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
(CMS Books in Mathematics, Ouvrages de mathématiques de la SMC. ISSN:21974152)

版	1st ed. 2011.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2011
大きさ	XIV, 822 p. 40 illus : online resource
著者標目	*Fabian, Marián author Habala, Petr author Hájek, Petr author Montesinos, Vicente author Zizler, Václav author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Topology FREE:Functional Analysis FREE:Topology
一般注記	Preface -- 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 -- C^1 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 -- References -- Symbol Index -- Subject Index -- Author Index 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 HTTP:URL=https://doi.org/10.1007/978-1-4419-7515-7

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