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.
General
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