Introduction to Banach Spaces: Analysis and Probability

Inbunden, Engelska, 2017

Del 167 i serien Cambridge Studies in Advanced Mathematics

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Beskrivning

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. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

Produktinformation

Utgivningsdatum:2017-11-02
Mått:158 x 235 x 27 mm
Vikt:670 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:402
Förlag:Cambridge University Press
ISBN:9781107162624
Översättare:Danièle Gibbons, Greg Gibbons, Danièle Gibbons, Daniele Gibbons

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Daniel Li is a Professor at Université d'Artois, France. Hervé Queffélec is Emeritus Professor at Université de Lille I, France. He has published over 60 papers, two research books, and four textbooks, including Twelve Landmarks of Twentieth-Century Analysis (Cambridge, 2015).

Recensioner i media

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

Innehållsförteckning

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.