The general structure of the decoherence-free subalgebra for uniformly continuous quantum Markov semigroups

By using the decomposition of the decoherence-free subalgebra N(T) in direct integrals of factors, we obtain a structure theorem for every uniformly continuous quantum Markov semigroup. Moreover, we prove that when there exists a faithful normal invariant state, N(T) has to be atomic and decoherence takes place.