Strengthened Stone-Weierstrass type theorem

Tyt. z nagłówka.Bibliogr. s. 649-650.Dostępny również w formie drukowanej.ABSTRACT: The aim of the paper is to prove that if L is a linear subspace of the space C(K) of all real-valued continuous functions defined on a nonempty compact Hausdorff space K such that min(/ƒ/, 1) Є L whenever fnof; Є L, then for any nonzero g Є L (where L denotes the uniform closure of L in C(K)) and for any sequence (bn) ∞/n=1 of positive numbers satisfying the relation [formula] there exists a sequence [formula] of elements of L such that //ƒn// = bn for each n ≥ 1, g = [formula] and /g/œ = [formula]. Also the formula for L is given. KEYWORDS: stone-weierstrass theorem, function lattices