Classical and Quantum Semigroups
Classical and Quantum Semigroups
Several quantum Markov semigroups admit an invariant abelian subalgebra which can be looked at as an algebra of bounded functions on some measurable space. The restriction to this subalgebra is a semigroup of positive and identity preserving operators i.e. a classical Markov semigroup (see Examples 3.3, 3.4).