Introduction to Banach Spaces: Analysis and Probability
Introduction to Banach Spaces: Analysis and Probability
Hervé Queffélec, Université de Lille I
Danièle Gibbons
Greg Gibbons
AUD$169.95
inc GSTThis 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
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
Product details
December 2017Hardback
9781107162624
402 pages
235 × 158 × 27 mm
0.67kg
2 b/w illus. 50 exercises
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.
