General Properties of the Liouville Operator

We study the self-adjointness of the Liouvillianof a symmetric operator. We also discuss some cases ofthe spectrum of the Liouville operator of a self-adjointHamiltonian with purely continuous singular spectrum. The presence of an absolutelycontinuous part for the spectrum of Liouvillianscorresponding to Hamiltonians with purely continuoussingular spectrum shows that quantum theory in Hilbertand Liouville spaces is not equivalent.