positive operators and approximation in function spaces on completely regular spaces
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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
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|---|---|
| Authors | ;Francesco Altomare;Sabrina Diomede |
| Journal | structural engineering and mechanics |
| Year | 2003 |
| DOI |
10.1155/S0161171203301206
|
| URL | |
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