Proceedings of the American Mathematical Society

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



Free Araki-Woods factors and Connes' bicentralizer problem

Author: Cyril Houdayer
Journal: Proc. Amer. Math. Soc. 137 (2009), 3749-3755
MSC (2000): Primary 46L10, 46L54
Published electronically: May 21, 2009
MathSciNet review: 2529883
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that for any type $ {\rm III_1}$ free Araki-Woods factor $ \mathcal{M} = \Gamma(H_{\mathbf{R}}, U_t)''$, the bicentralizer of the free quasi-free state $ \varphi_U$ is trivial. Using Haagerup's Theorem, it follows that there always exists a faithful normal state $ \psi$ on $ \mathcal{M}$ such that $ (\mathcal{M}^\psi)' \cap \mathcal{M} = \mathbf{C}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L10, 46L54

Retrieve articles in all journals with MSC (2000): 46L10, 46L54

Additional Information

Cyril Houdayer
Affiliation: Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095
Address at time of publication: CNRS-ENS Lyon, UMPA UMR 5669, 69364 Lyon cedex 7, France

Keywords: Free Araki-Woods factors, Connes' bicentralizer problem
Received by editor(s): October 7, 2008
Received by editor(s) in revised form: February 16, 2009
Published electronically: May 21, 2009
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society