Morita Equivalences for Completely Positive Linear Maps and GNS-C*-Correspondences

We define the notion of (strong) Morita equivalence of completely positive linear maps from a unital C∗-algebra to the C∗-algebra of (bounded) adjointable operators on a right Hilbert C∗-module. For pairs of mutually (strong) Morita equivalent unital C∗-algebras, we construct a bijective correspondence between the corresponding sets of Morita equivalence classes of completely positive linear maps and we discuss the relation of Morita equivalences for completely positive linear maps and GNS-C∗- correspondences.