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arXiv · 0809.3827

Free Araki-Woods factors and Connes' bicentralizer problem

Cyril Houdayer
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Abstract

We show that for any free Araki-Woods factor $\mathcal{M} = \Gamma(H_\R, U_t)"$ of type ${\rm III_1}$, 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 $(\mathcal{M}^\psi)' \cap \mathcal{M} = \C$.

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Cyril Houdayer. 2008-09-22. Free Araki-Woods factors and Connes' bicentralizer problem. https://doi.org/10.1090/s0002-9939-09-09923-7

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