We prove that, for any type free product factor, its continuous core is full if and only if its -invariant is the usual topology on the real line. This trivially implies, as a particular case, the same result for free Araki–Woods factors. Moreover, our method shows the same result for full (generalized) Bernoulli crossed product factors of type .
"A characterization of the fullness of continuous cores of type free product factors." Kyoto J. Math. 56 (3) 599 - 610, September 2016. https://doi.org/10.1215/21562261-3600193