Overview
- Notes and exercises related to the topic
- Presents open problems and possible directions of research in each chapter
Part of the book series: CMS Books in Mathematics (CMSBM)
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Table of contents (8 chapters)
Keywords
About this book
One of the fundamental questions of Banach space theory is whether every Banach space has a basis. A space with a basis gives us a sense of familiarity and concreteness, and perhaps a chance to attempt the classification of all Banach spaces and other problems.
The main goals of this book are to: -introduce the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces, -aim the text at graduate students and researchers who have a foundation in Banach space theory, - expose the reader to some current avenues of research in biorthogonal systems in Banach spaces, -provide notes and exercises related to the topic, suggest open problems and possible new directions of research.
Numerous exercises are included, and the only prerequisites are a basic background in functional analysis.
Reviews
From the reviews:
"This monograph is devoted to the study of the different types of coordinate systems that may exist in infinite-dimensional Banach spaces. … will certainly become a great reference book for specialists in nonseparable Banach space theory. Its contents are comprehensive and perfectly up to date. Very recent results are included and several proofs are simplified and given with their optimal form. It must be mentioned that this book is also accessible to graduate students and young researchers willing to discover this area." (Gilles Lancien, Mathematical Reviews, Issue 2008 k)
"The book under review contains a clear, detailed and self-contained exposition of the modern state-of-the-art in the biorthogonal systems theory. … one of their goals is to attract young mathematicians to Banach space theory. In my opinion, the book perfectly serves this purpose. … Every chapter contains an exercises section. Exercises … are supplied with hints and references to the corresponding literature."(Vladimir Kadets, Zentralblatt MATH, Vol. 1136 (14), 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Biorthogonal Systems in Banach Spaces
Authors: Petr Hájek, Vicente Montesinos Santalucía, Jon Vanderwerff, Václav Zizler
Series Title: CMS Books in Mathematics
DOI: https://doi.org/10.1007/978-0-387-68915-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2008
Hardcover ISBN: 978-0-387-68914-2Published: 15 November 2007
Softcover ISBN: 978-1-4419-2395-0Published: 08 September 2011
eBook ISBN: 978-0-387-68915-9Published: 04 October 2007
Series ISSN: 1613-5237
Series E-ISSN: 2197-4152
Edition Number: 1
Number of Pages: XVIII, 339