We prove that every positive trace on a countably generated ∗-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial ∗-algebra can be embedded into a metric ultraproduct of generic matrix algebras. As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded into an ultraproduct...

In the paper we extent the notion of Dobrushin coefficient of ergodicity for positive contractions defined on L-space associated with finite von Neumann algebra, and in terms of this coefficient we prove stability results for L-contractions.

We prove that the normal cohomology groups H w(M, K(H)) of a von Neumann algebra M with coefficients in the algebra of compact operators are zero if M is atomic of type Ifin. In addition, the completely bounded normal cohomology groups H wcb(B(H), K(H)) are shown to be 0 as well.

Suppose M is a von Neumann algebra with normal, tracial state ϕ and {a 1 ,. .. , a n } is a set of self-adjoint elements of M. We provide an alternative uniform packing description of δ 0