History of Banach Spaces and Linear Operators

Albrecht Pietsch0817643672, 0817645969, 9780817643676, 9780817645960

Named for Banach, who was one of the great mathematicians of the twentieth century, the concept of Banach spaces figures 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.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. While other historical texts on the subject focus on developments before 1950, this one is mainly devoted to the second half of the 20th 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 for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor. Helpful information is provided for professors in preparing their own lectures on functional analysis.

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Table of contents :
Preface……Page 12
Notation and Terminology……Page 16
Introduction……Page 17
Contents……Page 5
The Birth of Banach Spaces……Page 22
Historical Roots and Basic Results……Page 46
Topological Concepts – Weak Topologies……Page 77
Classical Banach Spaces……Page 107
Basic Results from the Post-Banach Period……Page 179
Modern Banach Space Theory – Selected Topics……Page 309
Miscellaneous Topics……Page 571
Mathematics Is Made by Mathematicians……Page 610
Chronology……Page 694
Original Quotations……Page 701
Bibliography……Page 704
Textbooks and monographs……Page 705
Historical and biographical books……Page 730
Collected and selected works……Page 733
Collections……Page 737
Seminars……Page 743
Anonymous works……Page 744
Mathematical papers……Page 746
Historical and biographical papers……Page 843
Coauthors……Page 851
Index……Page 855