Partition-dependent stochastic measures and -deformed cumulants.
Pointwise Convergence Theorems in L2 over a von Neumann Algebra.
Positive cones associated with a von Neumann algebra.
Positive operator bimeasures and a noncommutative generalization
For C*-algebras A and B and a Hilbert space H, a class of bilinear maps Φ: A× B → L(H), analogous to completely positive linear maps, is studied. A Stinespring type representation theorem is proved, and in case A and B are commutative, the class is shown to coincide with that of positive bilinear maps. As an application, the extendibility of a positive operator bimeasure to a positive operator measure is shown to be equivalent to various conditions involving positive scalar bimeasures, pairs of...
Positive self-adjoint extensions of operators affiliated with a von Neumann algebra.
Probability interpolating between free and boolean [Book]
Probability measures corresponding to Aval numbers
We describe the class of probability measures whose moments are given in terms of the Aval numbers. They are expressed as the multiplicative free convolution of measures corresponding to the ballot numbers .
Product-type non-commutative polynomial states
In [AnsMonic, AnsBoolean], we investigated monic multivariate non-commutative orthogonal polynomials, their recursions, states of orthogonality, and corresponding continued fraction expansions. In this note, we collect a number of examples, demonstrating what these general results look like for the most important states on non-commutative polynomials, namely for various product states. In particular, we introduce a notion of a product-type state on polynomials, which covers all the non-commutative...
Produit croisé d'une algèbre de Kac par un groupe localement compact
Projections from a von Neumann algebra onto a subalgebra
Pure Jauch-Piron states on von Neumann algebras