DENSITY OF INFIMUM-STABLE CONVEX CONES

Let X be a compact Hausdorff space and let A be a linear subspace of C(X; R) containing the constant functions, and separating points from probability measures. Then the inf-lattice generated by A is uniformly dense in C(X; R) . We show that this is a corollary of the Choquet-Deny Theorem, thus simplifying the proof and extending to the nonmetric case a result of McAfee and Reny.121117517

A GENERALIZED BERNSTEIN APPROXIMATION THEOREM

o TEXTO COMPLETO DESTE ARTIGO, ESTARÁ DISPONÍVEL À PARTIR DE AGOSTO DE 2015.104231733

FIXED-POINT THEOREMS FOR SET-VALUED MAPPINGS AND EXISTENCE OF BEST APPROXIMANTS

5444945

THE WEIERSTRASS-STONE THEOREM IN ABSOLUTE VALUED DIVISION RINGS

Let S be a zero-dimensional compact Hausdorff space and let E be a normed space over a non-Archimedean absolute valued division ring (K, \ . \). The space C(S; E) of all continuous functions from S into E is equipped with the uniform topology given by the supremum norm. A Weierstrass-Stone Theorem for arbitrary subsets of C(S;E) is established.41717

Approximation and interpolation from modules

A result about simultaneous approximation and interpolation from modules of weighted spaces is established. As a consequence, it is applied to certain polynomial algebras of the space of continuous bounded vector-valued functions equipped with the strict topology.244185892993