On central sequence algebras of tensor product von Neumann algebras

Yasuhito Hashiba

We show that when $M,N_1,N_2$ are tracial von Neumann algebras with $M^{\prime }\cap M^{\omega }$ abelian, $M^{\prime }\cap (M\bar{\otimes }{N}_1{)}^{\omega }$ and $M^{\prime }\cap (M\bar{\otimes }{N}_2{)}^{\omega }$ commute in $(M\bar…