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A Short Course on Banach Space Theory


Part of London Mathematical Society Student Texts

  • Date Published: December 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521603720

$ 53.95

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About the Authors
  • 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.

    • Based on a tried-and-tested classroom approach
    • The course has minimal prerequisites - accessible to anyone who has had a standard first course in graduate analysis
    • The course is self-contained with numerous exercises, a preliminaries section and an appendix on topology
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    Reviews & endorsements

    '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

    • Date Published: December 2004
    • format: Paperback
    • isbn: 9780521603720
    • length: 198 pages
    • dimensions: 229 x 151 x 11 mm
    • weight: 0.3kg
    • availability: Available
  • Table of Contents

    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.

  • Author

    N. L. Carothers, Bowling Green State University, Ohio

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