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 II1 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 = LFn LFm and φi is any sequence of faithful normal states on M, then the l-various (M,φ1) * ... * (M,φl) are all mutually non-isomorphic.
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