Asymptotic formulae for positive linear operators on convex subsets of normed spaces

We establish an asymptotic formula for general sequences of positive linear operators acting on spaces of continuous functions de¯ned on convex subsets of (possibly in¯nite-dimensional) Banach spaces. Moreover we deduce analogous formulae for the Bernstein-Schnabl operators on bounded convex subsets of separable Banach spaces, as well as for the multidimensional extension of the so-called Sz¶asz-Mirakjan operators.