We define unbounded,
completely positive, operator valued linear maps on C∗-algebras, and investigate
their natural order structure. Following F. Combes, J. Math. Pure et Appl., we study
the quasi equivalence, equivalence and type of the Stinespring representations
associated with unbounded completely positive maps. Following A. van Daele,
Pacific J. Math., we study an unbounded completely positive map α with
dense domain which is invariant under a group G of *-automorphisms and
construct a G-invariant projection map ϕ′ of the set ℱ of continuous completely
positive maps dominated by α, onto the set ℱ0 of G-invariant elements
of ℱ0. This is used to derive various properties of the upper envelope of
ℱ0.
