On some density theorems in regular vector lattices of continuous functions

• Autores: Francesco Altomare, Mirella Cappelletti Montano
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 58, Fasc. 2, 2007, págs. 131-149
• Idioma: inglés
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• Resumen

  • In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of continuous functions defined 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 socalled generalized affine 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.