A free product pair rigidity result in von Neumann algebras

Abstract

We prove that the free product pair of any finitely many copies of the unique amenable type III${}_1$ factor endowed with weakly mixing states remembers the number of free components and the given states.

15 pages; to appear in JNCG

References in corpus (2)

• On a Class of Type II${}_1$ Factors with Betti Numbers Invariants
• Structure of modular invariant subalgebras in free Araki-Woods factors