On some density theorems in regular vector lattices of continuous functions.

Altomare, Francesco, and Cappelletti Montano, Mirella. "On some density theorems in regular vector lattices of continuous functions.." Collectanea Mathematica 58.2 (2007): 131-149. <http://eudml.org/doc/41801>.

@article{Altomare2007,
abstract = {In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of continuous functions de ned on a locally compact Hausdorff space, which we introduced and studied in [3,4] and which we named regular vector lattices. In this framework, by using properties of the subspace of the so-called generalized af ne functions, we give a simple description of the closed vector sublattice, the closed Stone vector sublattice and the closed subalgebra generated by a subset of a regular vector lattice.As a consequence, we obtain some density results. Finally, a connection with the Korovkin type approximation theory is also shown.},
author = {Altomare, Francesco, Cappelletti Montano, Mirella},
journal = {Collectanea Mathematica},
keywords = {Espacios de funciones lineales; Retículos; Teorema de Stone-Weierstrass; Stone-Weierstrass theorem; sublattice; Korovkin set},
language = {eng},
number = {2},
pages = {131-149},
title = {On some density theorems in regular vector lattices of continuous functions.},
url = {http://eudml.org/doc/41801},
volume = {58},
year = {2007},
}

TY - JOUR
AU - Altomare, Francesco
AU - Cappelletti Montano, Mirella
TI - On some density theorems in regular vector lattices of continuous functions.
JO - Collectanea Mathematica
PY - 2007
VL - 58
IS - 2
SP - 131
EP - 149
AB - In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of continuous functions de ned on a locally compact Hausdorff space, which we introduced and studied in [3,4] and which we named regular vector lattices. In this framework, by using properties of the subspace of the so-called generalized af ne functions, we give a simple description of the closed vector sublattice, the closed Stone vector sublattice and the closed subalgebra generated by a subset of a regular vector lattice.As a consequence, we obtain some density results. Finally, a connection with the Korovkin type approximation theory is also shown.
LA - eng
KW - Espacios de funciones lineales; Retículos; Teorema de Stone-Weierstrass; Stone-Weierstrass theorem; sublattice; Korovkin set
UR - http://eudml.org/doc/41801
ER -