A note on cocycle-conjugate endomorphisms of von Neumann algebras

Abstract

We show that two cocycle-conjugate endomorphisms of an arbitrary von Neumann algebra that satisfy certain stability conditions are conjugate endomorphisms, when restricted to some specific von Neumann subalgebras. As a consequence of this result, we obtain a new criterion for conjugacy of Powers shift endomorphisms acting on factors of type I ∞ . \rm {I}_{\infty }.