Introduction to Banach spaces : analysis and probability
 Responsibility
 Daniel Li, Université d'Artois, France, Hervé Queffélec, Université de Lille I, France ; translated from the French by Danièle Gibbons and Greg Gibbons.
 Uniform Title
 Introduction à l'étude des espaces de Banach. English
 Publication
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018.
 Physical description
 2 volumes : illustrations ; 24 cm.
 Series
 Cambridge studies in advanced mathematics ; 166167. 09506330
Access
Available online
Science Library (Li and Ma)
Stacks
Library has: v.12
Call number  Status 

QA322.2 .L5 2018 V.1  Unknown 
QA322.2 .L5 2018 V.2  Unknown 
More options
Creators/Contributors
 Author/Creator
 Li, Daniel author.
 Contributor
 Queffélec, Hervé, author.
 Gibbons, Daniele, translator.
 Gibbons, Greg, translator.
Contents/Summary
 Contents

 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 infinitedimensional Banach spaces in the past twenty years G. Godefroy An update on some problems in high dimensional convex geometry and related probabilistic results O. Guedon A few updates and pointers G. Pisier On the mesh condition for Sidon sets L. RodriguezPiazza Bibliography Author index Notation index Subject index.
 (source: Nielsen Book Data)9781107162624 20180115
 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. psumming operators. Applications 7. Some properties of Lpspaces 8. The space l1 Annex. Banach algebras, compact Abelian groups Bibliography Author index Notation index Subject index.
 (source: Nielsen Book Data)9781107160514 20180115
 Volume 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. psumming operators. Applications 7. Some properties of Lpspaces 8. The Space l1 Annex. Banach algebras, compact abelian groups Bibliography Author index Notation index Subject index. Volume 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 infinitedimensional Banach spaces in the past twenty years G. Godefroy An update on some problems in high dimensional convex geometry and related probabilistic results O. Guedon A few updates and pointers G. Pisier On the mesh condition for Sidon sets L. RodriguezPiazza Bibliography Author index Notation index Subject index.
 (source: Nielsen Book Data)9781107162631 20180115
 Publisher's Summary
 This twovolume 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.
(source: Nielsen Book Data)9781107162631 20180115
Subjects
Bibliographic information
 Publication date
 2018
 Series
 Cambridge studies in advanced mathematics ; 166167
 Note
 "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.
 ISBN
 9781107162631 (hardback : 2 Volume Set)
 1107162637 (hardback : 2 Volume Set)
 9781107160514 (hardback : v. 1)
 1107160510 (hardback : v. 1)
 9781107162624 (hardback : v. 2)
 1107162629 (hardback : v. 2)