History of Banach Spaces and Linear Operators

Named for Banach, one of the great mathematicians of the twentieth century, the concept of Banach spaces figures prominently in the study of functional analysis with applications to integral and differential equations, approximation theory, harmonic analysis, convex geometry, numerical mathematics, analytic complexity, and probability theory.

"Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. 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. The book may serve as a reference for researchers and as an introduction for graduate students 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."

The Birth of Banach Spaces.- Historical Roots and Basic Results.- Topological Concepts - 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.