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Banach Space TheoryThe Basis for Linear and Nonlinear Analysis

Series: CMS Books in Mathematics

Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.

1st Edition., 2011, XIV, 822 p. 40 illus.

• 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
• Offers sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more
  

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.
Content Level » Graduate
Keywords » Radon-Nikodým property - functional analysis - infinite-dimensional Banach space theory
Related subjects » Analysis - Geometry & Topology