A Note on the Approximation by a Sum of Two Algebras

We consider the problem of approximation of a continuous function $$f$$ defined on a compact metric space $$X$$ by elements from a sum of two algebras. We prove a de la Vallée Poussin type theorem, which estimates the approximation error $$E(f)$$ from below. We also obtain a duality formula for the precise computation of $$E(f)$$ .