By applying the results of the first part of the paper, we establish some Korovkin-type theorems for continuous positive linear operators in the setting of regular vector lattices of continuous functions. Moreover, we present simple methods to construct Korovkin subspaces for finitely defined operators and for the identity operator and we determine those classes of operators which admit finite-dimensional Korovkin subspaces. Finally, we give a Korovkin-type theorem for continuous positive projections.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-4,
author = {Francesco Altomare and Mirella Cappelletti Montano},
title = {Regular vector lattices of continuous functions and Korovkin-type theorems-Part II},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {69-90},
zbl = {1105.46012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-4}
}
Francesco Altomare; Mirella Cappelletti Montano. Regular vector lattices of continuous functions and Korovkin-type theorems-Part II. Studia Mathematica, Tome 173 (2006) pp. 69-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-4/