Introduction to Banach spaces : analysis and probability. Volume 1 / Daniel Li, Hervé Queffélec ; translated from the French by Danièle Gibbons and Greg Gibbons.

Originally published in French as Introduction à l'étude des espaces de Banach by Société Mathématique de France, 2004.

Title from publisher's bibliographic system (viewed on 10 Nov 2017).

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.