Advertisement

Sequences and Series in Banach Spaces

  • Joseph Diestel

Part of the Graduate Texts in Mathematics book series (GTM, volume 92)

Table of contents

  1. Front Matter
    Pages iii-xii
  2. Joseph Diestel
    Pages 17-23
  3. Joseph Diestel
    Pages 24-31
  4. Joseph Diestel
    Pages 32-57
  5. Joseph Diestel
    Pages 58-65
  6. Joseph Diestel
    Pages 66-123
  7. Joseph Diestel
    Pages 192-199
  8. Joseph Diestel
    Pages 200-218
  9. Joseph Diestel
    Pages 219-225
  10. Joseph Diestel
    Pages 241-255
  11. Back Matter
    Pages 257-263

About this book

Introduction

This volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac­ titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.

Keywords

Banach Banach Space Banachscher Raum Convexity Sequences Series Spaces choquet integral compactness differential equation extrema

Authors and affiliations

  • Joseph Diestel
    • 1
  1. 1.Department of Math SciencesKent State UniversityKentUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5200-9
  • Copyright Information Springer-Verlag New York 1984
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-9734-5
  • Online ISBN 978-1-4612-5200-9
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site