Free Araki-Woods factors and Connes' bicentralizer problem

Abstract

We show that for any free Araki-Woods factor $\mathcal{M}=\Gamma (H_{\mathbb{R}},U_t)"$ of type $\mathrm{II}{\mathrm{I}}_1$, the bicentralizer of the free quasi-free state ${\phi }_U$ is trivial. Using Haagerup's Theorem, it follows that there always exists a faithful normal state $\psi$ on $\mathcal{M}$ such that $(\mathcal{M}^ψ)' \cap \mathcal{M} = \C$.

8 pages

References in corpus (1)

• On multiplicity and free absorption for free Araki-Woods factors

Cited by in corpus (7)

• Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors
• Unique prime factorization and bicentralizer problem for a class of type III factors
• Structural results for free Araki-Woods factors and their continuous cores
• On the factoriality of q-deformed Araki-Woods von Neumann algebras
• Classification of a family of non almost periodic free Araki-Woods factors
• Structure of bicentralizer algebras and inclusions of type III factors
• Connes' bicentralizer problem for q-deformed Araki-Woods algebras