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Hypercontractivity in noncommutative holomorphic spaces
 Commun. Math. Phys
, 2005
"... ABSTRACT. We prove an analog of Janson’s strong hypercontractivity inequality in a class of noncommutative “holomorphic ” algebras. Our setting is the qGaussian algebras Γq associated to the qFock spaces of Bozejko, Kümmerer and Speicher, for q ∈ [−1, 1]. We construct subalgebras Hq ⊂ Γq, a qSeg ..."
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Cited by 8 (6 self)
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ABSTRACT. We prove an analog of Janson’s strong hypercontractivity inequality in a class of noncommutative “holomorphic ” algebras. Our setting is the qGaussian algebras Γq associated to the qFock spaces of Bozejko, Kümmerer and Speicher, for q ∈ [−1, 1]. We construct subalgebras Hq ⊂ Γq, a qSegalBargmann transform, and prove Janson’s strong hypercontractivity L 2 (Hq) → L r (Hq) for r an even integer. 1.
Fidaleo F. Unique mixing of the shift on the C ∗ –algebras generated by the q–canonical commutation relations
 Houston J. Math
"... Abstract. The shift on the C ∗ –algebras generated by the Fock representation of the q–commutation relations has the strong ergodic property of unique mixing, when q  < 1. 1. introduction The q–commutation relations have been studied in the physics literature, see e.g. [8]. These are the relati ..."
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Cited by 1 (0 self)
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Abstract. The shift on the C ∗ –algebras generated by the Fock representation of the q–commutation relations has the strong ergodic property of unique mixing, when q  < 1. 1. introduction The q–commutation relations have been studied in the physics literature, see e.g. [8]. These are the relations aia + j − qa+ j ai = δij1, i, j ∈ Z where −1 ≤ q ≤ 1. This gives an interpolation between the canonical commutation relations (Bosons) when q = 1 and the canonical anticommutation relations (Fermions) when q = −1, while when q = 0 we have freeness (cf. [16]). In [3], (see also [9] and [7]) a Fock representation of these relations was found, giving annihilators ai and their adjoints, the creators a + i, acting on a Hilbert space with a vacuum vector Ω. The C ∗ –algebras and von Neumann algebras generated by sets of these operators or by their real parts ai+a + i have
The von Neumann algebra generated by tgaussians
, 2006
"... We study the tdeformation of gaussian von Neumann algebras. When the number of generators is fixed, it is proved that if t sufficiently close to 1, then these algebras do not depend on t. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness. 1 ..."
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Cited by 1 (0 self)
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We study the tdeformation of gaussian von Neumann algebras. When the number of generators is fixed, it is proved that if t sufficiently close to 1, then these algebras do not depend on t. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness. 1
U.F.R des Sciences et Techniques
, 2006
"... Asymptotic matricial models and QWEP property for qArakiWoods algebras ..."