Introduction to banach spaces : analysis and probability

Author(s)

• Li, Daniel
• Queffelec, H.
• Gibbons, Danièle
• Gibbons, Greg

Bibliographic Information

Introduction to banach spaces : analysis and probability

Daniel Li, Hervé Queffélec ; translated from the French by Danièle Gibbons and Greg Gibbons

（Cambridge studies in advanced mathematics, 166-167）

Cambridge University Press, 2018

• : set : hardback
• v. 1 : hbk
• v. 2 : hbk

Other Title

Introduction à l'étude des espaces de Banach

Note

Translation of: Introduction à l'étude des espaces de Banach

"Originally published in French as "Introduction à l'étude des espaces de Banach" by Société Mathématique de France, 2004"--T.p. verso

Includes bibliographical references and indexes

Description and Table of Contents

Volume

v. 1 : hbk ISBN 9781107160514

Description

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.

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.

Volume

: set : hardback ISBN 9781107162631

Description

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.

Table of Contents

• 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. 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. 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 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. Guedon
• A few updates and pointers G. Pisier
• On the mesh condition for Sidon sets L. Rodriguez-Piazza
• Bibliography
• Author index
• Notation index
• Subject index.

by "Nielsen BookData"

Details

• NCID: BB25126225
• ISBN:
  • 9781107162631
  • 9781107160514
  • 9781107162624
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: fre
• Place of Publication: Cambridge
• Pages/Volumes: 2 v.
• Size: 24 cm
• Classification:
  • DC23 : 515.732
• Subject Headings:
  • LCSH : Banach spaces
• Parent Bibliography ID:
  • BA00109761