Modified Bernstein-Schnabl operators on convex compact subsets of locally convex spaces and their limit semigroups

In this paper we introduce a sequence (Mn)nn0 of positive linear operators as a modification of the Bernstein-Schnabl operators associated with a positive projection on C(K), where K is a convex compact subset of a locally convex space; moreover we study its main approximation and qualitative properties. Furthermore, we establish an asymptotic formula for those operators, and we prove that to the sequence (Mn)nn0 there corresponds a uniquely determined C0-semigroup (in some special case a Feller one) which is representable as a limit of suitable powers of the operators.