Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A Kurosh-type theorem for type III factors

Author: Jason Asher
Journal: Proc. Amer. Math. Soc. 137 (2009), 4109-4116
MSC (2000): Primary 46L10, 46L09
Published electronically: July 20, 2009
MathSciNet review: 2538572
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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 $ \{\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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Jason Asher
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095

Received by editor(s): November 13, 2008
Received by editor(s) in revised form: March 8, 2009
Published electronically: July 20, 2009
Additional Notes: Research supported in part by NSF grant DMS-0555680 and NSF VIGRE grant DMS-0701302.
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.