Faithful Representations of Crossed Products by Endomorphisms

Abstract

Stacey has recently characterised the crossed product A xaTS of a C*-algebra A by an endomorphism a as a C*-algebra whose representations are given by covariant representations of the system (A, a).Following work of O'Donovan for automorphisms, we give conditions on a covariant representation (71, S) of (A, a) which ensure that the corresponding representation 7txSof/4xaNis faithful.We then use this result to improve a theorem of Paschke on the simplicity of A xQ N .