A Kurosh-Type Theorem for Type III Factors

Abstract: 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.