Khadijeh Karimi, Kamran Sharifi : Completely positive maps on Hilbert modules over pro-C*-algebras p. 181-193


We derive Paschke's GNS construction for completely positive maps on unital pro-C*-algebras from the KSGNS construction, presented by M. Joita [J. London Math. Soc. 66 (2002), 421-432], and then we deduce an analogue of Stinespring theorem for Hilbert modules over pro-C*-algebras. Also, we obtain a Radon-Nikodym type theorem for operator valued completely positive maps on Hilbert modules over pro-C*-algebras.

Key Words: Pro-C*-algebras, Hilbert modules, completely positive maps, Stinespring theorem, Radon-Nikodym theorem.

2010 Mathematics Subject Classification: Primary 46L05, Secondary 46L08, 46K10.