On tensor products of completely positive linear maps between pro-C *-algebras

In this paper we define the tensor products of completely positive linear maps between pro-C^*-algebras and discuss about connection between the KSGNS construction associated with the strict completely positive linear maps ρ and θ and the KSGNS construction associated with ρ ⊗ θ. This research was partially supported by CEEX grant -code PR-D11-PT00-48/2005 from The Romanian Ministry of Education and Research and partially by CNCSIS (Romanian National Council for Research in High Education) grant-code A 1065/2006.