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International Mathematics Research Papers (2006) Vol. 2006 : article ID 76978, 87 pages, doi:10.1155/IMRP/2006/76978
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

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

M. Junge

Department of Mathematics, University of Illinois Urbana, IL 61801, USA E-mail address: junge{at}math.uiuc.edu

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


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