A Kurosh-type theorem for type III factors

Asher, Jason

doi:10.1090/S0002-9939-09-10009-6

A Kurosh-type theorem for type III factors
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Proc. Amer. Math. Soc. 137 (2009), 4109-4116 Request permission

Abstract:

We prove a generalization of N. Ozawa’s Kurosh-type theorem to the setting of free products of semiexact $\text {II}_1$ 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 $\{\varphi _i\}$ is any sequence of faithful normal states on $M$, then the $l$-various $(M,\varphi _1) * ... * (M,\varphi _l)$ are all mutually non-isomorphic.

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