Restrictions of CP-Semigroups to Maximal Commutative Subalgebras

摘要

We give a necessary and sufficient criterion when a normal CP-map on a vonNeumann algebra admits a restriction to a maximal commutative subalgebra. Weapply this result to give a far reaching generalization of Rebolledo'ssufficient criterion for the Lindblad generator of a Markov semigroup on B(G).