Radon-Nikodym type theorem for alpha-completely positive maps

Abstract

We introduce a new notion of alpha-completely positive map on a C*-algebra as a generalization of the notion of completely positive map. Then we study a theorem of the Radon-Nikodym type that there is a one-to-one correspondence between alpha-completely positive maps and positive operators and, as an application of the Radon-Nikodym type theorem, we give a characterization of pure alpha-completely positive maps. Finally, we study a covariant version of the Stinespring's theorem for a covariant alpha-completely positive map (see Theorem 4.3).