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: CP-maps) on locally C ∗ -algebras. In this article suitable notion of minimality construction has been identified so as to ensure uniqueness up unitary equivalence the associated representation. Using Radon–Nikodym type proved. Further, unbounded operator valued Hilbert modules over -algebras (also called CP-inducing maps) presented. Following M. Joiţa, shown. both cases derivative is contraction some complex space with an upward filtered family reducing subspaces.