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.
On some density theorems in regular vector lattices of continuous functions
ALTOMARE, Francesco;CAPPELLETTI MONTANO, MIRELLA
2007-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
