GENERAL-PROPERTIES OF THE LIOUVILLE OPERATOR

We study the self-adjointness of the Liouvillian of a symmetric operat or. We also discuss some cases of the spectrum of the Liouville operat or of a self-adjoint Hamiltonian with purely continuous singular spect rum. The presence of an absolutely continuous part for the spectrum of Liouvillians corresponding to Hamiltonians with purely continuous sin gular spectrum shows that quantum theory in Hilbert and Liouville spac es is nor equivalent.