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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Free Araki-Woods factors and Connes’ bicentralizer problem
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by Cyril Houdayer
Proc. Amer. Math. Soc. 137 (2009), 3749-3755
DOI: https://doi.org/10.1090/S0002-9939-09-09923-7
Published electronically: May 21, 2009

Abstract:

We show that for any type $\mathrm {III}_1$ 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
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Bibliographic 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
  • Email: cyril@math.ucla.edu, cyril.houdayer@umpa.ens-lyon.fr
  • 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
  • © Copyright 2009 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 3749-3755
  • MSC (2000): Primary 46L10, 46L54
  • DOI: https://doi.org/10.1090/S0002-9939-09-09923-7
  • MathSciNet review: 2529883