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In this paper the relations between various semigroups of operators and between various infinitesimal operators connected with a homogeneous in t Markov process are investigated. General conditions are established under which the Markov process is determined by its corresponding infinitesimal operator. Let Uₜ be a semigroup of linear operators in the Banach space L such that \|Uₜ \| 1. Let Tₜ = Uₜ be an adjoint semigroup in the conjugate space B = L^ *. More abstractly the main object of this paper can be characterized as the study of semigroups Tₜ and its infinitesimal operators in strong and weak topologies of space B.
E. B. Dynkin (Sun,) studied this question.