Graduate Texts in Mathematics

Topics in Banach Space Theory

Authors: Albiac, Fernando, Kalton, Nigel J.

  • The approach taken is the unifying viewpoint of basic sequences

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eBook $64.99
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  • ISBN 978-0-387-28142-1
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Softcover $84.95
price for USA
  • ISBN 978-1-4419-2099-7
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About this Textbook

Assuming only a basic knowledge of functional analysis, the book gives the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. The aim of this text is to provide the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems.
Fernando Albiac received his PhD in 2000 from Universidad Publica de Navarra, Spain. He is currently Visiting Assistant Professor of Mathematics at the University of Missouri,
Columbia. Nigel Kalton is Professor of Mathematics at the University of Missouri, Columbia. He has written over 200 articles with more than 82 different co-authors, and most recently, was the recipient of the 2004 Banach medal of the Polish Academy of Sciences.

Reviews

From the reviews:

"Geometry of Banach Spaces is a quite technical field which requires a fair practice of sharp tools from every domain of analysis. … The authors of the book under review succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly. … the book is essentially self-contained. It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated … . I strongly recommend to every graduate student … ." (Gilles Godefroy, Mathematical Reviews, Issue 2006 h)

"This book gives a self-contained overview of the fundamental ideas and basic techniques in modern Banach space theory. … In this book one can find a systematic and coherent account of numerous theorems and examples obtained by many remarkable mathematicians. … It is intended for graduate students and specialists in classical functional analysis. … I think that any mathematician who is interested in geometry of Banach spaces should … look over this book. Undoubtedly, the book will be a useful addition to any mathematical library." (Peter Zabreiko, Zentralblatt MATH, Vol. 1094 (20), 2006)

"This book provides a sequel treatise on classical and modern Banach space theory. It is mainly focused on the study of classical Lebesgue spaces Lp, sequence spaces lp, and Banach spaces of continuous functions. … There is a comprehensive bibliography (225 items). The book is understandable and requires only a basic knowledge of functional analysis … . It can be warmly recommended to a broad spectrum of readers – to graduate students, young researchers and also to specialists in the field." (EMS Newsletter, March, 2007)


Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-0-387-28142-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.95
price for USA
  • ISBN 978-1-4419-2099-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topics in Banach Space Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
233
Copyright
2006
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-28142-1
DOI
10.1007/0-387-28142-8
Softcover ISBN
978-1-4419-2099-7
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XI, 376
Topics