Beschreibung:
Named for one of the great mathematicians of the twentieth century, Banach spaces figure prominently in the study of functional analysis, having applications to integral and differential equations, approximation theory, harmonic analysis, convex geometry, numerical mathematics, analytic complexity, and probability theory. This work, written by a distinguished specialist in functional analysis, is devoted to a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. While other comprehensive texts on Banach spaces focus on developments before 1950, this one is mainly devoted to the second half of the twentieth century. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. Numerous examples and counterexamples elucidate the scope of the underlying concepts. As a stimulus for further research, the text also contains many problems which have not been previously solved. The book may serve as a reference and introduction for graduate students and researchers who want to learn Banach space theory with some historical flavor. TOC:Preface * Acknowledgements * Introduction * The Birth of Banach Spaces * Historical Roots and Basic Results * Weak Topologies * Classical Banach Spaces * Basic Results from the Post-Banach Period * Modern Banach Space Theory - Selected Topics * Miscellaneous Topics * Mathematics is Made by Mathematicians * Chronology * Quotations * Bibliography * Index