Non-factorizable extensions of the Liouville operator: the Friedrichs model

We construct for the Friedrichs model extensions of the Liouville operator which do not reduce to any extension of the corresponding Hamilton operator. These extensions originate in the Brussels–Austin approach to irreversibility and acquire meaning in suitable rigged Hilbert spaces (RHS) associated with the Hilbert–Schmidt space, known as rigged Liouville space (RLS).