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arXiv · 1006.3689

Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors

Cyril Houdayer·Eric Ricard
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Abstract

We show that all the free Araki-Woods factors $Γ(H_\R, U_t)"$ have the complete metric approximation property. Using Ozawa-Popa's techniques, we then prove that every nonamenable subfactor $\mathcal{N} \subset Γ(H_\R, U_t)"$ which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type ${\rm III_1}$ factors constructed by Connes in the '70s can never be isomorphic to any free Araki-Woods factor, which answers a question of Shlyakhtenko and Vaes.

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Cyril Houdayer, Eric Ricard. 2011-07-28. Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors. https://doi.org/10.1016/j.aim.2011.06.010

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