Positive operators and approximation in function spaces on completely regular spaces
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...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203301206 |
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| _version_ | 1832558087323516928 |
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| author | Francesco Altomare Sabrina Diomede |
| author_facet | Francesco Altomare Sabrina Diomede |
| author_sort | Francesco Altomare |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2f16fde1007341928d74742335e7a903 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2f16fde1007341928d74742335e7a9032025-02-03T01:33:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003613841387110.1155/S0161171203301206Positive operators and approximation in function spaces on completely regular spacesFrancesco Altomare0Sabrina Diomede1Department of Mathematics, University of Bari, Via Orabona 4, Bari 70125, ItalyDepartment of Economic Sciences, University of Bari, Via C. Rosalba 53, Bari 70124, ItalyWe 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.http://dx.doi.org/10.1155/S0161171203301206 |
| spellingShingle | Francesco Altomare Sabrina Diomede Positive operators and approximation in function spaces on completely regular spaces International Journal of Mathematics and Mathematical Sciences |
| title | Positive operators and approximation in function spaces on completely regular spaces |
| title_full | Positive operators and approximation in function spaces on completely regular spaces |
| title_fullStr | Positive operators and approximation in function spaces on completely regular spaces |
| title_full_unstemmed | Positive operators and approximation in function spaces on completely regular spaces |
| title_short | Positive operators and approximation in function spaces on completely regular spaces |
| title_sort | positive operators and approximation in function spaces on completely regular spaces |
| url | http://dx.doi.org/10.1155/S0161171203301206 |
| work_keys_str_mv | AT francescoaltomare positiveoperatorsandapproximationinfunctionspacesoncompletelyregularspaces AT sabrinadiomede positiveoperatorsandapproximationinfunctionspacesoncompletelyregularspaces |