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.

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

About the Author
Daniel Li is a Professor at Universite d'Artois, France. Herve Queffelec is Emeritus Professor at Universite de Lille I. He has published over sixty papers, two research books, and four textbooks, including Twelve Landmarks of Twentieth-Century Analysis (2015).

Reviews
Review of previous edition: 'carefully written and edited... The exposition is clear, precise and lively, and the text makes very good reading.' Eve Oja, Zentralblatt Math
Review of previous edition: 'Undoubtedly, the book will be very useful for all mathematicians (not only for postgraduate students) who work in the theory of Banach spaces, harmonic analysis and probability theory.' Anatolij M. Plichko, American Mathematical Society
'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



Book Information
ISBN 9781107160514
Author Daniel Li
Format Hardback
Page Count 460
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 750g
Dimensions(mm) 235mm * 158mm * 29mm