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Interactions between quantum probability and operator space theory

  • UMR de Mathématiques

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Abstract

We give a brief aspect of interactions between quantum probability and operator space theory by emphasizing the usefulness of noncommutative Khintchine type inequalities in the latter theory. After a short introduction to operator spaces, we present various Khintchine type inequalities in the noncommutative setting, including those for Rademacher variables, Voiculescu's semicircular systems and Shlyakhtenko's generalized circular systems. As an illustration of quantum probabilistic methods in operator spaces, we prove Junge's complete embedding of Pisier's OH space into a noncommutative L 1, for which Khintchine inequalities for the generalized circular systems are a key ingredient.

Original languageEnglish
Title of host publicationQuantum Potential Theory
PublisherSpringer Verlag
Pages117-159
Number of pages43
ISBN (Print)9783540693642
DOIs
StatePublished - 2008
Externally publishedYes

Publication series

NameLecture Notes in Mathematics
Volume1954
ISSN (Print)0075-8434

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