A note on the approximation by a sum of two algebras

Abstract

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 $E(f)$.

10 pages, typos corrected, references added; this paper includes material from arXiv:2204.07448