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 structures 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.
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