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Interactions between Quantum Probability and Operator Space Theory

  • Quanhua Xu
Part of the Lecture Notes in Mathematics book series (LNM, volume 1954)

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 non-commutative 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.

Keywords

Banach Space Operator Space Quantum Probability Complex Interpolation Operator Hilbert Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Quanhua Xu
    • 1
  1. 1.UFR Sciences et techniquesUniversité de Franche-ComtéBesançon CedexFrance

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