Conjugate Dynamical Systems on C*-algebras

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 $A\times_{\alpha}\mathbb Z_+$ and $B\times_{\beta}\mathbb Z_+$ 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.