A characterization of fullness of continuous cores of type III${}_1$ free product factors

Abstract

We prove that, for any type III${}_1$ free product factor, its continuous core is full if and only if its $\tau$-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 III${}_1$.

8 pages

References in corpus (2)

• Classification of type III Bernoulli crossed products
• Asymptotic structure of free Araki-Woods factors

Cited by in corpus (2)

• Bi-exact groups, strongly ergodic actions and group measure space type III factors with no central sequence
• Fullness and Connes' $\mathbf{\tau }$ invariant of type III tensor product factors