Daniel Li

Introduction to Banach Spaces: Analysis and Probability: Volume 1 (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 2. November 2017
• Englisch
• ISBN-13: 9781108300070
• Artikelnr.: 66177565

Autorenporträt

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

Inhaltsangabe

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.

Rezensionen

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