Positive operators and approximation in function spaces on completely regular spaces

Francesco Altomare and Sabrina Diomede

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-31

Abstract:

We discuss the approximation properties of nets of positive linear operators acting on function spaces defined on Hausdorff completely regular spaces. A particular attention is devoted to positive operators which are defined in terms of integrals with respect to a given family of Borel measures. We present several applications which, in particular, show the advantages of such a general approach. Among other things, some new Korovkin-type theorems on function spaces on arbitrary topological spaces are obtained. Finally, a natural extension of the so-called Bernstein-Schnabl operators for convex (not necessarily compact) subsets of a locally convex space is presented as well.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:360196

DOI: 10.1155/S0161171203301206

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