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.
@article{urn:eudml:doc:41801,
title = {On some density theorems in regular vector lattices of continuous functions.},
journal = {Collectanea Mathematica},
volume = {58},
year = {2007},
pages = {131-149},
zbl = {1127.46018},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41801}
}
Altomare, Francesco; Cappelletti Montano, Mirella. On some density theorems in regular vector lattices of continuous functions.. Collectanea Mathematica, Tome 58 (2007) pp. 131-149. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41801/