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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203301206 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |