Martingales in Banach Spaces

by Gilles Pisier

Overview

This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this self-contained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses.

Product Details

ISBN-13:	9781107137240
Publisher:	Cambridge University Press
Publication date:	06/06/2016
Series:	Cambridge Studies in Advanced Mathematics , #155
Pages:	580
Product dimensions:	6.18(w) x 9.25(h) x 1.42(d)

About the Author

Gilles Pisier is Emeritus Professor at the University of Paris VI, where he worked from 1981 to 2010. He is also a Distinguished Professor and holder of the Owen Chair in Mathematics at Texas A&M University. His international prizes include the Salem Prize in harmonic analysis (1979), the Ostrowski Prize (1997), and the Stefan Banach Medal (2001). He is a member of the Paris Académie des Sciences, a Foreign member of the Polish and Indian Academies of Science, and a Fellow of both the IMS and the AMS. He is also the author of several books, notably The Volume of Convex Bodies and Banach Space Geometry (Cambridge, 1989) and Introduction to Operator Space Theory (Cambridge, 2003).

Table of Contents

Introduction; Description of the contents; 1. Banach space valued martingales; 2. Radon Nikodým property; 3. Harmonic functions and RNP; 4. Analytic functions and ARNP; 5. The UMD property for Banach spaces; 6. Hilbert transform and UMD Banach spaces; 7. Banach space valued H1 and BMO; 8. Interpolation methods; 9. The strong p-variation of martingales; 10. Uniformly convex of martingales; 11. Super-reflexivity; 12. Interpolation and strong p-variation; 13. Martingales and metric spaces; 14. Martingales in non-commutative LP *.

Editorial Reviews

'This book is devoted to various aspects affirming the importance of martingale techniques throughout the development of modern Banach space theory. … The book is self-contained and is quite accessible with only a basic functional analysis background. In particular, it does not assume any prior knowledge of scalar-valued martingale theory. … It is this reviewer’s opinion that this excellent book will appeal to a wide audience and will become a classic reference in martingale theory.' Narcisse Randrianantoanina, Mathematical Reviews

From the Publisher