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

Francesco Altomare; Mirella Cappelletti Montano

Collectanea Mathematica (2007)

- Volume: 58, Issue: 2, page 131-149
- ISSN: 0010-0757

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topAltomare, 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 -

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