DILATIONS FOR C^∗-DYNAMICAL SYSTEMS WITH ABELIAN GROUPS ON HILBERT C^∗-MODULES

In this paper we investigate the dilations of completely positive definite representations of C^∗-dynamical systems with abelian groups on Hilbert C^∗-modules. We show that if (A, G, α) is a C^∗-dynamical system with G an abelian group, then every completely positive definite covariant representation (π, φ, E) of (A, G, α) on a Hilbert C∗-module E admits an unitary dilation (πˆ, φˆ, Eˆ).