Revistes Catalanes amb Accés Obert (RACO)

On some density theorems in regular vector lattices of continuous functions

Francesco Altomare, Mirella Cappelletti Montano


In this paper, we establish some density theorems in the setting of particular locally convex vector lattices of ontinuous 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 so-called 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.

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