A duality principle for rational approximation (Q1061959)

Let \(E\subseteq C(K)\) be a subspace of continuous functions defined on a compact Hausdorff space K. We characterize those spaces for which the rational functions with denominators and numerators from E are dense. Despite the non-linear structure of rational functions, this characterization uses only methods from linear functional analysis. As special cases, we recover various results on the density of Müntz rationals.