Overview

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.

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9781107162631

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Reviews

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 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 '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

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 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 '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 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 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 '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

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 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

Author Information

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).

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