On the invertibility of Moller morphisms

Local perturbations of the dynamics of infinite quantum systems are considered. It is known that, if the Moller morphisms associated to the dynamics and its perturbation are invertible, the perturbed evolution is isomorphic to the unperturbed one, and thereby shares its ergodic properties. It was claimed by V. Ya. Golodets [Theor. Math. Phys. 23,525 (1975)] that the above
condition holds whenever the observable algebra is asymptotically abelian for the unperturbed evolution, and the perturbed evolution has a KMS state. The present paper contains a counterexample to this statement, and a construction of a spatial representation of the Moller
morphisms.