Trotter’s approximation of semigroups and order of convergence in C2,α-spaces

We improve the quantitative estimate of the convergence in Trotter's approximation theorem and obtain a representation of the resolvent operators in terms of iterates of linear operators on its whole domain. We are able to apply these results in the very general context of Bernstein-Schnabl operators in an infinite dimensional setting. In the finite dimensional context of the standard simplex we give some estimates for functions of class C^{2,\alpha} which considerably improve some previous estimates and allow to establish a partial inverse result.