KSGNS type construction for $\alpha $-completely positive maps on Krein   $C^{\ast}$-modules
  In this paper, we investigate $\Phi$-maps associated to a certain type of $\alpha$-completely positive maps. We then prove a KSGNS (Kasparov--Stinespring--Gel'fand--Naimark--Segal) type theorem for $\alpha $-completely positive maps on Krein $C^*$-modules and show that the minimal KSGNS construction is unique up to unitary equivalence. We also establish a covariant version of the KSGNS type theorem for a covariant $\alpha $-completely positive map and study the structure of minimal covariant KSGNS constructions. 
Mohammad Sal Moslehian, Maria Joita, Un Cig Ji
math.OA math-ph math.FA math.MP