Banach Space Theory: The Basis for Linear and Nonlinear Analysis (CMS Books in Mathematics)

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.

Review
From the reviews: “The material touches all the usual introductory topics plus such areas as tensor products, smoothness and other geometric issues, optimization, structure, etc. It is as current as a book this massive and wide-ranging can be. … it is a critical addition to the library of any college that has functional analysts of any stripe on its campus. … Summing Up: Essential. Graduate students and researchers/faculty.” (D. Robbins, Choice, Vol. 48 (11), July, 2011)