Overview
- Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory
- Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products
- Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more
- Includes information about further topics and directions of research and some open problems
- Includes supplementary material: sn.pub/extras
Part of the book series: CMS Books in Mathematics (CMSBM)
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Table of contents (17 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews:
“The material touches all the usual introductory topics plus such areas as tensor products, smoothness and other geometric issues, optimization, structure, etc. It is as current as a book this massive and wide-ranging can be. … it is a critical addition to the library of any college that has functional analysts of any stripe on its campus. … Summing Up: Essential. Graduate students and researchers/faculty.” (D. Robbins, Choice, Vol. 48 (11), July, 2011)
“The book is well-written and is essentially self-contained. All of the standard topics (as well as many other topics) are covered and the authors have accumulated a large collection of exercises on which students can hone their skills. … an impressive book that should be welcomed by students interested in learning the basic or more advanced topics in the theory of Banach spaces and by researchers in Banach spaces or related fields.” (Barry Turett, Zentralblatt MATH, Vol. 1229, 2012)
“It is designed to lead the reader from the basic concepts and principles to several streams of current research in Banach spaces. … I found the book very readable. It is clearly written and provides accessible references to many techniques that are commonly used in contemporary research in Banach space theory. … a nice book invaluable both for learning the topic and as a reference. This is definitely a book that anyone interested in Banach space theory (or functional analysis) should have on his/her desk.” (Sophocles Mercourakis, Mathematical Reviews, Issue 2012 h)
“This book is a German-style introduction to Banach Spaces. The authors have tried to include everything that might be useful in applications in optimization, PDEs, analysis … . if you need to know what a dentable Banach space is, you can find out here … . Most importantly, the book comes with a good set of indices, which should make it a useful reference.” (Fernando Q. Gouvêa, TheMathematical Association of America, June, 2011)
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Banach Space Theory
Book Subtitle: The Basis for Linear and Nonlinear Analysis
Authors: Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos, Václav Zizler
Series Title: CMS Books in Mathematics
DOI: https://doi.org/10.1007/978-1-4419-7515-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-1-4419-7514-0Published: 15 December 2010
Softcover ISBN: 978-1-4939-4114-8Published: 23 August 2016
eBook ISBN: 978-1-4419-7515-7Published: 04 February 2011
Series ISSN: 1613-5237
Series E-ISSN: 2197-4152
Edition Number: 1
Number of Pages: XIII, 820
Topics: Functional Analysis, Topology