arXiv subjects
Publications and source records attributed to Jason Asher.
We consider von Neumann algebras generated by the stationary laws of free stochastic differential equations of the form $dX_t = dS_t -1/2 DV(X_t)$ for a suitably convex multivariate noncommutative polynomial $V$. Using techniques of Guionnet and Shlyakhtenko, we prove that these von Neumann algebras have property AO of Ozawa and are thus solid.
We prove a generalization of N. Ozawa's Kurosh-type theorem to the setting of free products of semiexact II_1 factors with respect to arbitrary (non-tracial) faithful normal states. We are thus able to distinguish certain resulting type III factors. For example, if M = LF_n \otimes LF_m and {ϕ_i} is any sequence of faithful normal states on M, then the l-various (M,ϕ_1) * ... * (M,ϕ_l) are all mutually non-isomorphic.