Restrictions of CP-semigroups to maximal commutative subalgebras
Volume 78 / 2007
Banach Center Publications 78 (2007), 121-132
MSC: Primary 46L53, 46L55, 46L08; Secondary 60J25, 81S25.
DOI: 10.4064/bc78-0-8
Abstract
We give a necessary and sufficient criterion for a normal CP-map on a von Neumann algebra to admit a restriction to a maximal commutative subalgebra. We apply this result to give a far reaching generalization of Rebolledo's sufficient criterion for the Lindblad generator of a Markov semigroup on ${\scr B}(G)$.
