Entropie libre et algèbres d'opérateurs
Entropy considerations in the noncommutative setting.
Équations de structure des martingales et probabilités quantiques
Ergodic Actions by Compact Groups on C*-Algebras.
États quasi-libres libres et facteurs de type III
Les états quasi-libres sur l’algèbre des relations d’anticommutation canoniques donnent lieu à des représentations qui engendrent les facteurs moyennables d’Araki et Woods. Dans le cadre des probabilités libres de Voiculescu, Shlyakhtenko a trouvé un analogue libre de ces facteurs Araki-Woods. La construction de Shlyakhtenko part d’un groupe à un paramètre de transformations orthogonales d’un espace de Hilbert réel. Les facteurs associés fournissent une richesse de nouveaux exemples de facteurs...
Factorization of Operators Through Lp ... or Lp1 and Non-Commutative Generalizations.
Feuilletages et algèbres d'opérateurs
Frame functions, signed measures and completeness of inner product spaces
Free and classical entropy over the circle.
Free cumulants of some probability measures
Free dendriform algebras. I: A parenthesis setting.
Free diffusions, free entropy and free Fisher information
Free generalized gamma convolutions.
Free powers of the free Poisson measure
We compute moments of the measures , where ϖ denotes the free Poisson law, and ⊞ and ⊠ are the additive and multiplicative free convolutions. These moments are expressed in terms of the Fuss-Narayana numbers.
Free probability theory and non-crossing partitions.
Freeness with amalgamation, limit theorems and S-transform in non-commutative probability spaces of type B
The paper addresses several problems left open by P. Biane, F. Goodman and A. Nica [Trans. Amer. Math. Soc. 355 (2003)]. The main result is that a type B non-commutative probability space can be studied in the framework of freeness with amalgamation. This view allows easy ways of constructing a version of the S-transform as well as proving analogues to the Central Limit Theorem and Poisson Limit Theorem.
Fuss-Catalan numbers in noncommutative probability.
Geometric aspects of the Tomita-Takesaki theory I.
Geometric aspects of the Tomita-Takesaki theory II.
Gleason measures and some inner products on the algebra of bounded operators on a Hilbert space