The spectrum of the Liouville-von Neumann operator

We relate the pure point spectrum, the singularly continuous, and the absolutely continuous part of the spectrum of the Liouville-von Neumann operator [H,•] to the respective parts of the spectrum of the Hamiltonian operator H. As a consequence of this result we obtain a theorem about the weak * limit of the time evolution W(t) of a normal state W for t → ∞.