Regular vector lattices of continuous functions and Korovkin-type theorems-Part II

Francesco Altomare, and Mirella Cappelletti Montano. "Regular vector lattices of continuous functions and Korovkin-type theorems-Part II." Studia Mathematica 172.1 (2006): 69-90. <http://eudml.org/doc/284913>.

@article{FrancescoAltomare2006,
abstract = {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.},
author = {Francesco Altomare, Mirella Cappelletti Montano},
journal = {Studia Mathematica},
keywords = {positive operator; positive projection; finitely defined operator; Korovkin-type approximation theorem; vector lattice of continuous functions},
language = {eng},
number = {1},
pages = {69-90},
title = {Regular vector lattices of continuous functions and Korovkin-type theorems-Part II},
url = {http://eudml.org/doc/284913},
volume = {172},
year = {2006},
}

TY - JOUR
AU - Francesco Altomare
AU - Mirella Cappelletti Montano
TI - Regular vector lattices of continuous functions and Korovkin-type theorems-Part II
JO - Studia Mathematica
PY - 2006
VL - 172
IS - 1
SP - 69
EP - 90
AB - 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.
LA - eng
KW - positive operator; positive projection; finitely defined operator; Korovkin-type approximation theorem; vector lattice of continuous functions
UR - http://eudml.org/doc/284913
ER -