Hilbert C*-modules and projective representations associated with multipliers

Abstract

In this paper we consider projective sigma-representations and give the dilations associated with the representations. To unify the various representation theorem, we use the Kolmogorov decompositions for positive definite kernels. We present dilation theorems for projective sigma-representations, which generalize Stinespring dilation theorem for covariant completely positive maps as well as Naimark-Sz.-Nagy characterization of positive definite functions. We also construct a representation of a right Hilbert C*-module for a strictly U-covariant and completely positive map.