A Short Course on Banach Space Theory(London Mathematical Society Student Texts Series) / Edition 1

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Overview

This short course on classical Banach space theory is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas, such as harmonic analysis, the theory of frames and wavelets, signal processing, economics, and physics. The book is intended for use in an advanced topics course or seminar, or for independent study. It offers a more user-friendly introduction than can be found in the existing literature and includes references to expository articles and suggestions for further reading.
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Editorial Reviews

From the Publisher
'This lively written text focuses on certain aspects of the (neo-) classical theory of Banach spaces as developed in the 1950s and 1960s and is intended as an introduction to the subject, e.g., for future Ph.D. students. … This slim book is indeed very well suited to serve as an introduction to Banach spaces. Readers who have mastered it are well prepared to study more advanced texts such as P. Wojtaszczyk's Banach Spaces for Analysts (Cambridge University Press, second edition) or research papers.' Zentralblatt MATH

'… a painstaking attention both to detail in the mathematics and to accessibility for the reader. … You could base a good postgraduate course on it.' Bulletin of the London Mathematical Society

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Product Details

  • ISBN-13: 9780521603720
  • Publisher: Cambridge University Press
  • Publication date: 6/28/2010
  • Series: London Mathematical Society Student Texts
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 184
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.47 (d)

Table of Contents

Preface; 1. Classical Banach spaces; 2. Preliminaries; 3. Bases in Banach spaces; 4. Bases in Banach spaces II; 5. Bases in Banach spaces III; 6. Special properties of C0, l1, and l∞; 7. Bases and duality; 8. Lp spaces; 9. Lp spaces II; 10. Lp spaces III; 11. Convexity; 12. C(K) Spaces; 13. Weak compactness in L1; 14. The Dunford-Pettis property; 15. C(K) Spaces II; 16. C(K) Spaces III; A. Topology review.
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