Vol. 66, No. 2, 1976

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ISSN: 0030-8730
Unbounded completely positive linear maps on Cāˆ—-algebras

David E. Evans

Vol. 66 (1976), No. 2, 325ā€“346

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 ϕof the set of continuous completely positive maps dominated by α, onto the set 0 of G-invariant elements of 0. This is used to derive various properties of the upper envelope of 0.

Mathematical Subject Classification 2000
Primary: 46L05
Received: 1 December 1975
Published: 1 October 1976
David E. Evans