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]
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