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

M. Junge

doi:10.1155/IMRP/2006/76978

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

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Article number	76978
Journal	International Mathematics Research Papers
Volume	2006
DOIs	https://doi.org/10.1155/IMRP/2006/76978
State	Published - 2006
Externally published	Yes

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Mathematics(all)

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10.1155/IMRP/2006/76978

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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.",

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

Abstract

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