  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 {\phi_i} is any sequence
of faithful normal states on M, then the l-various (M,\phi_1) * ... *
(M,\phi_l) are all mutually non-isomorphic.
