Conjugate Dynamical Systems on C*-algebras

Abstract

Let $(A, α)$ and $(B, β)$ be C*-dynamical systems where $α$ and $β$ are arbitrary *-endomorphisms. When $α$ is injective or surjective, we show that the semicrossed products $A \times_α\mathbb{Z}$ and $B \times_β\mathbb{Z}$ are isometrically isomorphic if and only if $(A, α)$ and $(B, β)$ are outer conjugate. This conclusion also holds in various other cases as well.

19 pages