Introduction to Banach Spaces: Analysis and Probability

This second volume of a two-volume overview focuses on the applications of Banach spaces and recent developments in the field.

Daniel Li (Author), Hervé Queffélec (Author), Danièle Gibbons (Translated by), Greg Gibbons (Translated by)

9781107162624, Cambridge University Press

Hardback, published 2 November 2017

402 pages, 2 b/w illus. 50 exercises
23.5 x 15.8 x 2.7 cm, 0.67 kg

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

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. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

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.

Subject Areas: Stochastics [PBWL], Functional analysis & transforms [PBKF], Calculus & mathematical analysis [PBK]