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Orthonormal Systems and Banach Space Geometry

Part of Encyclopedia of Mathematics and its Applications

  • Authors:
  • Albrecht Pietsch, Friedrich-Schiller-Universität, Jena, Germany
  • Jörg Wenzel, Fraunhofer Institut Techno- und Wirtschaftsmathematik, Germany
  • Date Published: February 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521054317

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  • Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.

    • Deals in a unique way with harmonic and functional analysis
    • Contains a long list of problems which may serve as a starting point for research
    • Can be used as an advanced text
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    Reviews & endorsements

    'This work will certainly become a standard reference.' Zenbralblatt MATH

    ' … the book contains an enormous amount of information … it will serve as an invaluable reference book for years to come.' G. J. O. Jameson

    ' … this volume [is certain] to become a standard reference.' M. Grosser, Monatshefte für Mathematik

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    Product details

    • Date Published: February 2008
    • format: Paperback
    • isbn: 9780521054317
    • length: 564 pages
    • dimensions: 234 x 156 x 29 mm
    • weight: 0.78kg
    • contains: 11 b/w illus. 11 tables
    • availability: Available
  • Table of Contents

    Preface
    Introduction
    Preliminaries
    1. Ideal norms and operator ideals
    2. Ideal norms associated with matrices
    3. Ideal norms associated with orthonormal systems
    4. Rademacher and Gauss ideal norms
    5. Trigonometric ideal norms
    6. Walsh ideal norms
    7. Haar ideal norms
    8. Unconditionality
    9. Miscellaneous
    Summaries
    List of symbols
    Bibliography
    Index.

  • Authors

    Albrecht Pietsch, Friedrich-Schiller-Universität, Jena, Germany

    Jörg Wenzel, Fraunhofer Institut Techno- und Wirtschaftsmathematik, Germany

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