Interactions between Quantum Probability and Operator Space Theory
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.
KeywordsBanach Space Operator Space Quantum Probability Complex Interpolation Operator Hilbert Space
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