Generalized Kantorovich operators on Bauer simplices and their limit semigroups

In this paper, we prove an asymptotic formula for generalized Kantorovich operators associated with the canonical Markov pro- jection on a given Bauer simplex K . That formula involves an oper- ator acting on the subalgebra of all products of affine functions on K. Moreover, we prove that such an operator is closable and its closure is the generator of a Markov semigroup which, in turn, may be represented in terms of iterates of the above-mentioned generalized Kantorovich operators.