Introduction to Banach Spaces: Analysis and Probability 2 Volume Hardback Set (Series Numbers 166-167)

Two-volume overview of Banach spaces theory, emphasising its interplay with harmonic analysis (particularly Sidon sets) and probability.

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

9781107162631, Cambridge University Press

, published 2 November 2017

890 pages, 7 b/w illus. 140 exercises
23.5 x 15.8 x 5.5 cm, 1.43 kg

'This text is a welcome addition to the literature on Banach spaces. Parts of it may be used for advanced courses on Banach space theory, and a detailed reading will enlighten students and experts alike.' Ramon van Handel, Mathematical Reviews

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.

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