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. 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.
