Presenting an overview of most aspects of modern Banach space theory and its applications, this handbook offers up-to-date surveys by a range of expert authors. The surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory and partial differential equations. contains all the background needed for reading any other chapter. Each of the 21 articles after his is devoted to one specific direction of Banach space theory or its applications. Each article...

Springer-Verlag began publishing books in higher mathematics in 1920, when the series "Grundlehren der mathematischen " "Wissenschaften," initially conceived as a series of advanced textbooks, was founded by Richard Courant. A few years later a new series "Ergebnisse der Mathematik und ihrer " "Grenzgebiete," survey reports of recent mathematical research, was added.
Of over 400 books published in these series, many have become recognized classics and remain standard references for their subject. Springer is reissuing a selected few of these highly successful books in a new, inexpensive...

This volume presents a systematic and unified study of geometric nonlinear functional analysis. This area has its classical roots in the beginning of the 20th century and is a very active research area, having close connections to geometric measure theory, probability, classical analysis, combinatorics, and Banach space theory. The main theme of the book is the study of uniformly continuous and Lipschitz functions between Banach spaces (for example, differentiability, stability, approximation, existence of extensions and fixed points). This study leads naturally also to the classification of...