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© 2006

Topics in Banach Space Theory

  • The approach taken is the unifying viewpoint of basic sequences

Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 233)

About this book

Introduction

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.

Keywords

Banach Space Sequence space banach spaces functional analysis

Authors and affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA

Bibliographic information

  • Book Title Topics in Banach Space Theory
  • Authors Fernando Albiac
    Nigel J. Kalton
  • Series Title Graduate Texts in Mathematics
  • DOI https://doi.org/10.1007/0-387-28142-8
  • Copyright Information Springer Inc. 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-28141-4
  • Softcover ISBN 978-1-4419-2099-7
  • eBook ISBN 978-0-387-28142-1
  • Series ISSN 0072-5285
  • Edition Number 1
  • Number of Pages XI, 376
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Functional Analysis
  • Buy this book on publisher's site
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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)