On a class of ${\mathrm{II}}_1$ factors with at most one Cartan subalgebra

Narutaka Ozawa, Sorin Popa

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L({\mathbb{F}}_r)$ generates an amenable von Neumann subalgebra. Moreover, any II${}_1$ factor of th…