A short course on Banach space theory

書誌事項

A short course on Banach space theory

N.L. Carothers

(London Mathematical Society student texts, 64)

Cambridge University Press, 2005

  • : hard
  • : pbk

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注記

Bibliography: p.173-179

Includes index

内容説明・目次

内容説明

This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.

目次

  • 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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詳細情報

  • NII書誌ID(NCID)
    BA70876368
  • ISBN
    • 0521842832
    • 0521603722
  • LCCN
    2004045627
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    xii, 184 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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