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

We show that all the free Araki–Woods factors Γ ( H R , U t ) ″ have the complete metric approximation property. Using Ozawa–Popaʼs techniques, we then prove that every nonamenable subfactor N ⊂ Γ ( H R , U t ) ″ which is the range of a normal conditional expectation has no Cartan subalgebra. We finally deduce that the type III 1 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.