We show that the continuous core of any type III free product factor has no Cartan subalgebra. This is a complement to previous works due to Houdayer–Ricard and Boutonnet–Houdayer–Raum.
"Absence of Cartan subalgebras in continuous cores of free product von Neumann algebras." Proc. Japan Acad. Ser. A Math. Sci. 90 (10) 151 - 155, December 2014. https://doi.org/10.3792/pjaa.90.151