History of Banach Spaces and Linear Operators

This comprehensive book aims to cover the history of Banach spaces and operators (and not the history of mathematicians working in the field) and it is mainly focused on the second half of the 20th century. Nevertheless, the book starts with chapters on the birth of Banach spaces and their historical roots and basic results, followed by chapters on topological concepts (centred on weak topologies), including an overview of classical Banach spaces. The heart of the book (300 pages) consists of chapters on basic results from the post-Banach period and on selected topics of modern Banach space theory. The book ends (250 pages) with chapters on victims of politics, a description of scientific schools in Banach space theory, short biographies of some famous mathematicians and short sections including a list of the people working on Banach spaces who have been awarded the Fields Medal or who have been invited to lecture at the ICM and a list of names sorted by country. An extensive bibliography divided into several sections (textbooks, monographs, historical books, collected works, etc.) includes approximately 2600 items. The book can serve as a reference and guide with some historical flavour both for researchers and as an introduction for graduate students learning Banach space theory. As the author has made an enormous effort to cover the main trends of this part of functional analysis, it is quite natural that the content of the book reflects the taste of the author and that some parts of this field are not treated with enough detail. It is really a difficult task to describe in detail the contents of this voluminous book (of 855 pages). A very detailed review by J. Lindenstrauss can be found in Mathematical Reviews MR2300779.

Reviewer: 
jl
Book details
Author:  Publisher: 
Published: 
2007
ISBN: 
978-0-8176-4367-6
Price: 
EUR 109
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