Operator spaces and Araki-Woods factors --A quantum probabilistic approach--

Details Operator spaces and Araki-Woods factors --A quantum probabilistic approach-- Operator spaces and Araki-Woods factors --A quantum probabilistic approach--

2005-04-12

arxiv.org/abs/math/0504255v3

Mathematics

Operator Algebras

Scientific paper

We show that the operator Hilbert space OH introduced by Pisier embeds into the predual of the hyerfinite III1 factor. The main new tool is a Khintchine type inequality for the generators of the CAR algebra with respect to a quasi-free state. Our approach yields a Khintchine type inequality for the q-gaussian variables for all values q between -1 and 1. These results are closely related to recent results of Pisier and Shlyakhtenko in the free case.

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