34 research outputs found

    DENSITY OF INFIMUM-STABLE CONVEX CONES

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    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

    Uniform Closure of Tensor Product of Linear Subspaces

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    A GENERALIZED BERNSTEIN APPROXIMATION THEOREM

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

    ON VONNEUMANN VARIATION OF THE WEIERSTRASS-STONE THEOREM

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    Let X be a compact Hausdorff space and let D(X) be the set of all continuous real-valued functions f defined on X and such that 0 less-than-or-equal-to f(x) less-than-or-equal-to 1, for all x is-an-element-of X. The set D(X) is equipped with the uniform topology. We characterize the uniform closure of subsets A subset-of D(X) containing 0 and 1 and phi-psi + (1 - psi)eta, whenever they contain phi, psi and eta.134173234935

    THE WEIERSTRASS-STONE THEOREM IN ABSOLUTE VALUED DIVISION RINGS

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    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

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    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
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