  We prove some new characterisations of honesty of the perturbed semigroup in
Kato's Perturbation Theorem on abstract state spaces via three approaches,
namely mean ergodicity of operators, adjoint operators and uniqueness of the
perturbed semigroup. We then apply Kato's Theorem on abstract state spaces and
the honesty theory linked to it to the study of quantum dynamical semigroups.
We show that honesty is the natural generalisation of the notion of
conservativity.
