UNBOUNDED COMPLETELY POSITIVE LINEAR MAPS ON C*-ALGEBRAS

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 com-pletely positive maps. Following A. van Daele, Pacific J. Math., we study an unbounded completely positive map a with dense domain which is invariant under a group G of ^-automorphisms and construct a G-invariant projection map φ ' of the set 3F of continuous completely positive maps dominated by α, onto the set 3P0 of G-invariant elements of ^ 0. This is used to derive various properties of the upper envelope of 2FQ. 1. Introduction. W