Approximation properties and absence of Cartan subalgebra for free Araki-Woods factors
Abstract
We show that all the free Araki-Woods factors (H, Ut)" have the complete metric approximation property. Using Ozawa-Popa's techniques, we then prove that every nonamenable subfactor N ⊂ (H, Ut)" which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type III1 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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