2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225285We discuss the possibility of defining an algebraic dynamics within the settings of $O^\star$-algebras. Compared with our previous results on this subject, the main improvement here is that we are not assuming the existence of some hamiltonian for the {\em full} physical system. We will show that, under suitable conditions, the dynamics can still be defined via some limiting procedure starting from a given {\em regularized sequence}.Mathematical Physicstext