Stinespring's theorem for unbounded operator valued local completely positive maps and its applications
Dosiev (2008) obtained a Stinespring's theorem for local completely positive maps (in short: local CP-maps) on locally C∗-algebras. In this article a suitable notion of minimality for this construction has been identified so as to ensure uniqueness up to unitary equivalence for the associated representation. Using this a Radon–Nikodym type theorem for local completely positive maps has been proved. Further, a Stinespring's theorem for unbounded operator valued local completely positive maps on Hilbert modules over locally C∗-algebras (also called as local CP-inducing maps) has been presented. Following a construction of M. Joiţa, a Radon–Nikodym type theorem for local CP-inducing maps has been shown. In both cases the Radon–Nikodym derivative obtained is a positive contraction on some complex Hilbert space with an upward filtered family of reducing subspaces.
Bhat, B. V.Rajarama; Ghatak, Anindya; and Pamula, Santhosh Kumar, "Stinespring's theorem for unbounded operator valued local completely positive maps and its applications" (2021). Journal Articles. 2020.