Markov dilations on W∗-algebras

AbstractIn this paper a systematic study of Markov dilations is begun for completely positive operators on W∗-algebras which leave a faithful normal state invariant. It is shown that a minimal Markov dilation preserves important properties of the underlying completely positive operator. Afterwards some results are proved concerning the construction of dilations which lead to Markov dilations for large classes of operators. Finally some of the ideas developed here are applied to the study of a simple example over the 2 × 2 matrices