Factoriality of $q$-deformed Araki-Woods von Neumann algebras

It is proved that the $q$-Araki-Woods von Neumann algebras ${\mathrm{\Gamma }}_q({\text{CH}}_{\mathbb{R}},U_t{)}^{\mathrm{\prime }\mathrm{\prime }}$ for $q\in (-1,1)$ are factors if $dim({\text{CH}}_{\mathbb{R}})\ge 3$.