Introduction to Banach Spaces: Analysis and Probability: Volume 1

This first volume of a two-volume overview covers the basic theory of Banach spaces, harmonic analysis and probability.

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

9781107160514, Cambridge University Press

Hardback, published 2 November 2017

460 pages, 5 b/w illus. 95 exercises
23.5 x 15.8 x 2.9 cm, 0.75 kg

'The book contains a lot of interesting and deep results on Banach spaces and harmonic analysis treated, with the methods of probability theory. It can be used for advanced courses in functional analysis, but also by professional mathematicians as a valuable source of information.' S. Cobzas, Mathematica

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.

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.

Subject Areas: Probability & statistics [PBT], Functional analysis & transforms [PBKF], Calculus & mathematical analysis [PBK]