Formes multilinéaires dans les W*-algèbres.
Formes topologiques non commutatives
Frame functions, signed measures and completeness of inner product spaces
Fredholm Theories of Mixed Type with Analytic Index Functions.
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 dynamical quantum groups and the dynamical quantum group
We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the level of universal C*-algebras. As an example, we recover the dynamical studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.
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.
From double Lie groups to quantum groups
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
Functional calculus and spectral theory of locally C*-sums of locally m-convex C*-algebras
Fusion en algèbres de von Neumann et groupes de lacets
Fuss-Catalan numbers in noncommutative probability.