Examples of factors which have no Cartan subalgebras

We consider some conditions similar to Ozawa’s condition (AO), and prove that if a non-injective factor satisfies such a condition and has the W*CBAP, then it has no Cartan subalgebras. As a corollary, we prove that $\mathrm{I}{\mathrm{I}}_1$ factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type $\mathrm{I}\mathrm{I}{\mathrm{I}}_1$ factors with such a condition are semisolid as a $\mathrm{I}{\mathrm{I}}_{\mathrm{\infty }}$ factor.