We establish a simple criterion concerning the convergence of nets (or generalized sequences) of positive linear operators on $C(X)$, $X$ compact, toward a positive linear operator. As a consequence we discuss several criteria about the asymptotic behaviour of the iterates of Markov operators. Finally, we present some applications concerning the asymptotic behaviour of the iterates of Bernstein-Schnabl operators on a convex compact subset (not necessarily associated with a positive projection) and the iterates of a special linear operator generalizing the so-called Ces\`{a}ro operator on $C([0,1])$
On some convergence criteria for nets of positive operators on continuous function spaces
ALTOMARE, Francesco
2013-01-01
Abstract
We establish a simple criterion concerning the convergence of nets (or generalized sequences) of positive linear operators on $C(X)$, $X$ compact, toward a positive linear operator. As a consequence we discuss several criteria about the asymptotic behaviour of the iterates of Markov operators. Finally, we present some applications concerning the asymptotic behaviour of the iterates of Bernstein-Schnabl operators on a convex compact subset (not necessarily associated with a positive projection) and the iterates of a special linear operator generalizing the so-called Ces\`{a}ro operator on $C([0,1])$File in questo prodotto:
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