positive operators and approximation in function spaces on completely regular spaces

Clicks: 30
ID: 258802
2003
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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.
Reference Key
altomare2003internationalpositive Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors
Journal structural engineering and mechanics
Year 2003
DOI
10.1155/S0161171203301206
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