Provided M is a non-finite AFD-factor, it it shown that the action of a completely positive, state-pre-serving linear map (stochastic map) on normal states over M can always be reduced to a unitary mixing mapping with respect to a generating U.H.F.-subalgebra.
Cite this article
Peter M. Alberti, Completely Positive Stochastic Linear Maps Over AFD-Factors and Unitary Mixing on Generating U.H.F.-Subalgebras. Publ. Res. Inst. Math. Sci. 22 (1986), no. 6, pp. 1105–1117DOI 10.2977/PRIMS/1195177064