Completely positive maps on Hilbert modules over pro-C*-algebras

Abstract

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. {\bf 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.

15 pages, accepted. arXiv admin note: text overlap with arXiv:1611.04707

References in corpus (1)

• Induced representations of Hilbert modules over locally C*-algebras and the imprimitivity theorem