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.
- Traces the theory of Banach spaces from its origins to the present day
- Proves all the results from scratch
- Highlights how classical and harmonic analysis, and probability, interact with the theory of Banach spaces
Read more
Reviews & endorsements
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 from previous edition: '… carefully written and edited … The exposition is clear, precise and lively, and the text makes very good reading.' Eve Oja, Zentralblatt Math
See more reviews
Customer reviews

Not yet reviewed
Be the first to review

Log in to review

Review was not posted due to profanity
×

, create a review

(If you're not , sign out)

Please enter the right captcha value

Please enter a star rating.

Your review must be a minimum of 12 words.

How do you rate this item?

Reviews must contain at least 12 words about the product.

×

Product details
- Date Published: December 2017
- format: Hardback
- isbn: 9781107162624
- length: 402 pages
- dimensions: 235 x 158 x 27 mm
- weight: 0.67kg
- contains: 2 b/w illus. 50 exercises
- availability: Available
Table of Contents
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.
Look Inside
Authors
Daniel Li, Université d'Artois, France
Daniel Li is a Professor at Université d'Artois, France.
Hervé Queffélec, Université de Lille I
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).
Translators
Danièle Gibbons
Greg Gibbons
Contributors
G. Godefroy, O. Guédon, G. Pisier, L. Rodriguez-Piazza