Covariant completely positive linear maps between locally C*-algebras

Abstract

We prove a covariant version of the KSGNS (Kasparov, Stinespring, Gel'fand,Naimark,Segal) construction for completely positive linear maps between locally $C^{*}$-algebras. As an application of this construction, we show that a covariant completely positive linear map $ρ$ from a locally $C^{*}$-algebra $A$ to another locally $C^{*}$ -algebra $B$ with respect to a locally $C^{*}$-dynamical system $(G,A,α)$ extends to a completely positive linear map on the crossed product $A\times_{α^{}}G$.