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Topics in Banach Space Theory

  • Fernando Albiac
  • Nigel J. Kalton

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

Table of contents

  1. Front Matter
    Pages i-xx
  2. Fernando Albiac, Nigel J. Kalton
    Pages 1-27
  3. Fernando Albiac, Nigel J. Kalton
    Pages 29-50
  4. Fernando Albiac, Nigel J. Kalton
    Pages 51-75
  5. Fernando Albiac, Nigel J. Kalton
    Pages 77-107
  6. Fernando Albiac, Nigel J. Kalton
    Pages 109-136
  7. Fernando Albiac, Nigel J. Kalton
    Pages 137-176
  8. Fernando Albiac, Nigel J. Kalton
    Pages 177-208
  9. Fernando Albiac, Nigel J. Kalton
    Pages 209-233
  10. Fernando Albiac, Nigel J. Kalton
    Pages 235-257
  11. Fernando Albiac, Nigel J. Kalton
    Pages 259-293
  12. Fernando Albiac, Nigel J. Kalton
    Pages 295-309
  13. Fernando Albiac, Nigel J. Kalton
    Pages 311-335
  14. Fernando Albiac, Nigel J. Kalton
    Pages 337-359
  15. Fernando Albiac, Nigel J. Kalton
    Pages 361-426
  16. Fernando Albiac, Nigel J. Kalton
    Pages 427-444
  17. Back Matter
    Pages 445-508

About this book

Introduction

This text provides 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. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces.  This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them.

This textbook assumes only a basic knowledge of functional analysis, giving 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.

From the reviews of the First Edition:

"The authors of the book…succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly… It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments… I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book…"

—Gilles Godefroy, Mathematical Reviews

Keywords

Banach space theory continuous functions factorization theory greedy approximation lp-spaces nonlinear geometry of Banach spaces

Authors and affiliations

  • Fernando Albiac
    • 1
  • Nigel J. Kalton
    • 2
  1. 1.Departamento de MatemáticasUniversidad Pública de Navarra PamplonaSpain
  2. 2.University of Missouri, Columbia Dept. MathematicsColumbiaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-31557-7
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-31555-3
  • Online ISBN 978-3-319-31557-7
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site