Introduction to Banach Spaces: Analysis and Probability
Introduction to Banach Spaces: Analysis and Probability
Hervé Queffélec, Université de Lille I
Danièle Gibbons
Greg Gibbons
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.
- 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
Reviews & endorsements
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
Product details
May 2020Adobe eBook Reader
9781108300070
0 pages
5 b/w illus. 95 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Preface
- Preliminary chapter
- 1. Fundamental notions of probability
- 2. Bases in Banach spaces
- 3. Unconditional convergence
- 4. Banach space valued random variables
- 5. Type and cotype of Banach spaces. Factorisation through a Hilbert space
- 6. p-summing operators. Applications
- 7. Some properties of Lp-spaces
- 8. The space l1
- Annex. Banach algebras, compact Abelian groups
- Bibliography
- Author index
- Notation index
- Subject index.
