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

Abstract

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.