Of concern are some simple criteria about the convergence of sequences of positive linear operators and functionals in the framework of spaces of bounded functions which are continuous on a given subset of their domain. Among other things some applications concerning the behaviour of the iterates of Bernstein operators defined both on [0,1] as well as on the d-dimensional simplex and hypercube are discussed. A final section treats the behaviour of integrated arithmetic means with respect to a probability Borel measure on a convex compact subset K of a locally convex space. As a consequence a general weak law of large numbers for sequences of K-valued random variables is derived.
On the convergence of sequences of positive linear operators and functionals on bounded function spaces
Francesco Altomare
2021-01-01
Abstract
Of concern are some simple criteria about the convergence of sequences of positive linear operators and functionals in the framework of spaces of bounded functions which are continuous on a given subset of their domain. Among other things some applications concerning the behaviour of the iterates of Bernstein operators defined both on [0,1] as well as on the d-dimensional simplex and hypercube are discussed. A final section treats the behaviour of integrated arithmetic means with respect to a probability Borel measure on a convex compact subset K of a locally convex space. As a consequence a general weak law of large numbers for sequences of K-valued random variables is derived.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.