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Positive operators and approximation in function spaces on completely regular spaces

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  • Francesco Altomare
  • Sabrina Diomede

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.

Suggested Citation

  • Francesco Altomare & Sabrina Diomede, 2003. "Positive operators and approximation in function spaces on completely regular spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-31, January.
    • Handle: RePEc:hin:jijmms:360196
    DOI: 10.1155/S0161171203301206
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