Functional Analysis and Infinite-Dimensional Geometry [Paperback]

This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

Preface * 1 Basic Concepts in Banach Spaces * 2 Hahn-Banach and Banach Open Mapping Theorems * 3 Weak Topologies * 4 Locally Convex Spaces * 5 Structure of Banach Spaces * 6 Schauder Bases * 7 Compact Operators on Banach Spaces * 8 Differentiability of Norms * 9 Uniform Convexity * 10 Smoothness and Structure * 11 Weakly Compactly Generated Spaces * 12 Topics in Weak Toplogy * References * Index

From the reviews:

This is a substantial text containing up-to-date exposition and functional analysis from a Banach space point of view. It will be particularly useful for research investigation of nonlinear functional analysis and optimization&This book will stand as an important working text and reference and a significant guide for research students. (Mathematical Reviews)

This book can be warmly recommended to everyone interested in functional analysis, and Banach space theory in particular. It serves also as a textbook in courses for students in probability, physics, or engineering. Graduate students and researchers surely will find a lot of material from the field, as well as a source of inspiration. (European Mathematical Society Newsletter, September, 2003)

This is a substantial text containing an up-to-date exposition of functional analysis & . It will be particularly useful for research investigation of nonlinear functional analysis and optimization. & Each chapter ends with a remarkably weighty collection of exercises, many of which have useful hints at solutions appended to them & . the reader is directed throughout to the ample collection of references. The book will stanl£&