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

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Abstract

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.

Original languageEnglish (US)
Article number76978
JournalInternational Mathematics Research Papers
Volume2006
DOIs
StatePublished - 2006
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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