Introduction to Banach spaces : analysis and probability / Daniel Li, Université d'Artois, France, Hervé Queffélec, Université de Lille I, France ; translated from the French by Danièle Gibbons and Greg Gibbons.

Format:

Book

Author/Creator:

Li, Daniel, author.

Queffélec, Hervé, author.

Contributor:

Gibbons, Danièle, translator.

Gibbons, Greg, translator.

Series:

Cambridge studies in advanced mathematics ; 0950-6330 166-167.

Cambridge studies in advanced mathematics ; 166-167

Standardized Title:

Introduction à l'étude des espaces de Banach. English

Language:

English

French

Subjects (All):

Banach spaces.

Functional analysis.

Probabilities.

Measure theory.

Probability measures.

Numerical analysis.

Probability measures--Problems, exercises, etc.

Genre:

Problems and exercises.

Calendars.

Physical Description:

2 volumes : illustrations ; 24 cm.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018.

Summary:

This two-volume text provides a complete overview of the theory of Banach spaces, emphasizing 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. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

Contents:

V. 1 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.

v. 2 Preface; 1. Euclidean sections; 2. Separable Banach spaces without the approximation property; 3. Gaussian processes; 4. Reflexive subspaces of L1; 5. The method of selectors. Examples of its use; 6. The Pisier space of almost surely continuous functions. Applications; Appendix. News in the theory of infinite-dimensional Banach spaces in the past twenty years G. Godefroy; An update on some problems in high dimensional convex geometry and related probabilistic results O. Guédon; A few updates and pointers G. Pisier; On the mesh condition for Sidon sets L. Rodriguez-Piazza; Bibliography; Author index; Notation index; Subject index.

Notes:

"Originally published in French as Introduction à l'étude des espaces de Banach by Société Mathématique de France, 2004"--Title page verso.

"First published in English by Cambridge University Press 2018"--Title page verso.

Includes bibliographical references and indexes.

ISBN:

9781107162631

1107162637

9781107160514

1107160510

9781107162624

1107162629

OCLC:

1011095606