Dynamics in the state space and Heisenberg equations

It is shown that if the dynamical transformations form a group of affine bounded transformations on some full set of states and the generator of this group admits closure in the $w^*$ topology then the dynamic transformations are generated by Heisenberg equations on the algebra of observables with closed, densely defined Heisenberg operator that is the operator of unbounded differentiation on the algebra. The problem of extending a dynamics defined on some full folium of states to a larger class of states is considered briefly.