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

Publication year: 2011
Source: Advances in Mathematics, In Press, Corrected Proof, Available online 14 June 2011

Cyril, Houdayer , Éric, Ricard

We show that all the free Araki–Woods factors Γ(HR,Ut)″ have the complete metric approximation property. Using Ozawa–Popaʼs techniques, we then prove that every nonamenable subfactor 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 ʼ70s can never be isomorphic to any free Araki–Woods factor, which answers a question of Shlyakhtenko and Vaes.