  We consider a quantum channel acting on an infinite dimensional von Neumann
algebra of operators on a separable Hilbert space. When there exists an
invariant normal faithful state, the cyclic properties of such channels are
investigated passing through the decoherence free algebra and the fixed points
domain. Both these spaces are proved to be images of a normal conditional
expectation so that their consequent atomic structure are analyzed in order to
give a better description of the action of the channel and, for instance, of
its Kraus form and invariant densities.
