ON THE PROJECTIVE COVARIANT REPRESENTATIONS OF C*-DYNAMICAL SYSTEMS ASSOCIATED WITH COMPLETELY MULTI-POSITIVE PROJECTIVE u-COVARIANT MAPS

In this paper we prove that a completely multi-positive projective u-covariant linear map rho from A to L(B)(E) relative to the C*-dynamical system (G, A, alpha) induces a projective covariant representation (Phi(rho), v(rho), E(rho)) of (G, A, alpha) on a Hilbert C*-module over B. Then we show that a completely multi-positive projective u-covariant non-degenerate linear map from a C*-algebra A on a Hilbert C*-module E over a C*-algebra B can be extended to a completely multi-positive linear map on the twisted crossed product Ax(alpha)(omega)G. As a corollary we prove that, the representation of A x(alpha)(omega) G induced by the completely multi-positive projective u-covariant linear map rho is unitarily equivalent with the representation of A x(alpha)(omega) G induced by (Phi(rho), v(rho), E(rho)).