CMS Books in Mathematics

Biorthogonal Systems in Banach Spaces

Authors: Hajek, P., Montesinos Santalucia, V., Vanderwerff, J., Zizler, V.

  • Offers notes and exercises related to the topic
  • Presents open problems and possible directions of research in each chapter
  • Reviews current avenues of research in biorthogonal systems in Banach spaces
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eBook $69.99
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  • ISBN 978-0-387-68915-9
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Hardcover $99.00
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  • ISBN 978-0-387-68914-2
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  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
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  • ISBN 978-1-4419-2395-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

The main theme of this book is the relation between the global structure
of Banach spaces and the various types of generalized "coordinate
systems" - or "bases" - they possess.  This subject is not new and has
been investigated since the inception of the study of Banach spaces.  In
this book, the authors systematically investigate the concepts of
Markushevich bases, fundamental systems, total systems and their
variants. The material naturally splits into the case of separable
Banach spaces, as is treated in the first two chapters, and the
nonseparable case, which is covered in the remainder of the book.  This
book contains new results, and a substantial portion of this material
has never before appeared in book form.  The book will be of interest to
both researchers and graduate students.

Topics covered in this book include:

- Biorthogonal Systems in Separable Banach Spaces
- Universality and Szlenk Index
- Weak Topologies and Renormings
- Biorthogonal Systems in Nonseparable Spaces
- Transfinite Sequence Spaces
- Applications

Petr Hájek is Professor of Mathematics at the Mathematical Institute of
the Academy of Sciences of the Czech Republic.  Vicente Montesinos is
Professor of Mathematics at the Polytechnic University of
Valencia, Spain.  Jon Vanderwerff is Professor of Mathematics at La
Sierra University, in Riverside, California.  Václav Zizler is Professor
of Mathematics at the Mathematical Institute of the Academy of Sciences
of the Czech Republic.

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)


Table of contents (1 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-387-68915-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-0-387-68914-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-1-4419-2395-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Biorthogonal Systems in Banach Spaces
Authors
Series Title
CMS Books in Mathematics
Copyright
2008
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-68915-9
DOI
10.1007/978-0-387-68915-9
Hardcover ISBN
978-0-387-68914-2
Softcover ISBN
978-1-4419-2395-0
Series ISSN
1613-5237
Edition Number
1
Number of Pages
XVIII, 339
Topics