Tania-Luminita Costache : Projective version of Stinespring type theorems, p.109-124

Abstract:

The goal of this paper is to present a projective covariant version of Stinespring's theorem. We show that a projective covariant positive definite triple on a $C^{*}$-dynamical system $(G,A,\alpha)$ may be dilated to a projective covariant representation of $(G,A,\alpha)$. We find a projective covariant representation of a unital $C^{*}$-dynamical system $(G,A,\alpha)$ on a Hilbert $C^{*}$-module associated with a unital completely positive projective $u$-covariant linear map, extending Stinespring's theorem to Hilbert $C^{*}$-modules. We construct a projective covariant representation on a Hilbert $C^{*}$-module associated with a completely multi-positive projective $u$-covariant linear map.

Key Words: Multiplier, projective representation, projective covariant representation, projective $u$-covariant completely multi-positive linear map, positive definite function, $C^{*}$-dynamical system, Hilbert $C^{*}$-module.

2000 Mathematics Subject Classification: Primary: 20C25,
Secondary: 43A35, 22D10, 43A65, 22D25, 46L08.

Download the paper in pdf format here.