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Introduction to Banach Spaces: Analysis and Probability

Introduction to Banach Spaces: Analysis and Probability

Volume 1

£74.99

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: December 2017
  • availability: In stock
  • format: Hardback
  • isbn: 9781107160514

£ 74.99
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About the Authors
  • This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. In volume 2, four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

    • Traces the theory of Banach spaces from its origins to the present day
    • Proves all the results from scratch
    • Highlights how classical and harmonic analysis, and probability, interact with the theory of Banach spaces
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    Reviews & endorsements

    Review of previous edition: 'carefully written and edited... The exposition is clear, precise and lively, and the text makes very good reading.' Eve Oja, Zentralblatt Math

    Review of previous edition: 'Undoubtedly, the book will be very useful for all mathematicians (not only for postgraduate students) who work in the theory of Banach spaces, harmonic analysis and probability theory.' Anatolij M. Plichko, American Mathematical Society

    'The book contains a lot of interesting and deep results on Banach spaces and harmonic analysis treated, with the methods of probability theory. It can be used for advanced courses in functional analysis, but also by professional mathematicians as a valuable source of information.' S. Cobzas, Mathematica

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    Product details

    • Date Published: December 2017
    • format: Hardback
    • isbn: 9781107160514
    • length: 460 pages
    • dimensions: 235 x 158 x 29 mm
    • weight: 0.75kg
    • contains: 5 b/w illus. 95 exercises
    • availability: In stock
  • Table of Contents

    Preface
    Preliminary chapter
    1. Fundamental notions of probability
    2. Bases in Banach spaces
    3. Unconditional convergence
    4. Banach space valued random variables
    5. Type and cotype of Banach spaces. Factorisation through a Hilbert space
    6. p-summing operators. Applications
    7. Some properties of Lp-spaces
    8. The space l1
    Annex. Banach algebras, compact Abelian groups
    Bibliography
    Author index
    Notation index
    Subject index.

  • Authors

    Daniel Li, Université d’Artois, France
    Daniel Li is a Professor at Université d'Artois, France.

    Hervé Queffélec, Université de Lille I
    Hervé Queffélec is Emeritus Professor at Université de Lille I. He has published over sixty papers, two research books, and four textbooks, including Twelve Landmarks of Twentieth-Century Analysis (2015).

    Translators

    Danièle Gibbons

    Greg Gibbons

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