Abstract. We prove a Kurosh type theorem for free-product type II1 factors. In particular, if M = LF2 ¯⊗R, then the free-product type II1 factors M ∗... ∗ M are all prime and pairwise non-isomorphic. 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.

ABSTRACT. We prove an analog of Janson’s strong hypercontractivity inequality in a class of non-commutative “holomorphic ” algebras. Our setting is the q-Gaussian algebras Γq associated to the q-Fock spaces of Bozejko, Kümmerer and Speicher, for q ∈ [−1, 1]. We construct subalgebras Hq ⊂ Γq, a q-Segal-Bargmann transform, and prove Janson’s strong hypercontractivity L 2 (Hq) → L r (Hq) for r an even integer. 1.

We study the t-deformation 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

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

Noncommutative maximal ergodic theorems

Asymptotic matricial models and QWEP property for q-Araki-Woods algebras