A Covariant Representation Of A Partial C~*-Dynamical System

In this paper,let S be a unital inverse semigroup, A be a C~*-algebra,βbe an action of S on A,we show that a covariant version of the Stinespring representation for non-degenerate completely positive covariant with respect to a partial C~*—dynamical system linear mapsρfrom A to B(H), induce a covariant representation of (A, S,β) which is unique up to unitary equivalence.