Free Araki-Woods factors and Connes' bicentralizer problem

Details Free Araki-Woods factors and Connes' bicentralizer problem Free Araki-Woods factors and Connes' bicentralizer problem

2008-09-22

arxiv.org/abs/0809.3827v2

Proc. Amer. Math. Soc. 137 (2009), 3749-3755

Mathematics

Operator Algebras

8 pages

Scientific paper

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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