On the Lie-Trotter approximation formula

The paper presents a satisfactory version of the Lie-Trotter product formula in the context of the duality between a quasi-equicontinuos C0-semigroup {T(t)}t & GE;0 on a locally convex vector space X endowed with some locally convex Hausdorff topology r and its adjoint {T*(t)}t & GE;0 on the dual space X* endowed with the topology C(X*, X) of uniform convergence on compact subsets of Xr. An application is given for the transition semigroup of the diffusion associated to the generalized Schrodinger operator on L & INFIN;(RN, dx).& COPY; 2023 Elsevier B.V. All rights reserved.