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A Kurosh type theorem for type II1 factors
"... Abstract. We prove a Kurosh type theorem for freeproduct type II1 factors. In particular, if M = LF2 ¯⊗R, then the freeproduct type II1 factors M ∗... ∗ M are all prime and pairwise nonisomorphic. We also study the case of crossed product type II1 factors. This paper is a continuation of our prev ..."
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Cited by 13 (2 self)
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Abstract. We prove a Kurosh type theorem for freeproduct type II1 factors. In particular, if M = LF2 ¯⊗R, then the freeproduct type II1 factors M ∗... ∗ M are all prime and pairwise nonisomorphic. We also study the case of crossed product type II1 factors. This paper is a continuation of our previous papers [Oz2][OP], where the structure of (tensor products of) word hyperbolic group type II1 factors was studied. 1.
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.
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
A KUROSH TYPE THEOREM FOR TYPE II1 FACTORS
, 2004
"... The classification of type II1 factors (of discrete groups) was initiated by Murray and von Neumann [MvN] who distinguished the hyperfinite type II1 factor R from the group factor LFr of the free group Fr on r ≥ 2 generators. Thirty years later, Connes [Co2] proved uniqueness of the injective type I ..."
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The classification of type II1 factors (of discrete groups) was initiated by Murray and von Neumann [MvN] who distinguished the hyperfinite type II1 factor R from the group factor LFr of the free group Fr on r ≥ 2 generators. Thirty years later, Connes [Co2] proved uniqueness of the injective type II1 factor. Thus, the group
U.F.R des Sciences et Techniques
, 2006
"... Asymptotic matricial models and QWEP property for qArakiWoods algebras ..."