History of Banach Spaces and Linear Operators

Albrecht Pietsch

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Hardback

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English

Birkhauser Verlag
01 April 2007

Mathematics & Sciences; Functional analysis & transforms; History of mathematics

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.

By: Albrecht Pietsch
Imprint: Birkhauser Verlag
Country of Publication: United States
Dimensions: Height: 235mm, Width: 155mm, Spine: 46mm
Weight: 3.080kg
ISBN: 9780817643676
ISBN 10: 0817643672
Pages: 880
Publication Date: 01 April 2007
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for History of Banach Spaces and Linear Operators

"From the reviews: ""This fundamental and interesting monograph is devoted to the history (and not only) of a remarkable and rich branch of up-to-date mathematics... I recommend this book to all who are interested in Functional Analysis, to beginners and researchers, all students and all professors who deal with Functional Analysis and its applications. And I think that this book will be useful to each mathematical library.""—Zantralblatt Math ""Pietsch’s treatment of the early stages of Banach space theory and related areas is very nice and interesting. It contains much information I was not aware of before reading this book. … it can give the novice to the subject a good overview of what Banach space theory is about. … The book is written in a friendly style and is very readable. … I recommend this book to anyone interested in functional analysis … and even to the general mathematical community."" (Joram Lindenstrauss, Mathematical Reviews, Issue 2008 i) “There is a relatively large amount of works devoted to the prehistory of functional analysis and its birth in the classical Banach period, but this monograph is exceptional in its focus on the whole 20th century. … the author … has successfully brought together a respectable amount of material concerning Banach spaces and linear operators. … The book will be certainly useful not only to researchers, but also to students. … I can warmly recommend this book ‘to all who love Banach spaces.’” (Antonín Slavík, Mathematica Bohemica, Issue 2, 2010)"