Strengthened Stone-weierstrass Type Theorem
نویسنده
چکیده
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(|f |, 1) ∈ L whenever f ∈ L, then for any nonzero g ∈ L̄ (where L̄ denotes the uniform closure of L in C(K)) and for any sequence (bn)n=1 of positive numbers satisfying the relation P∞ n=1 bn = ‖g‖ there exists a sequence (fn) ∞ n=1 of elements of L such that ‖fn‖ = bn for each n > 1, g = P∞ n=1 fn and |g| = P∞ n=1 |fn|. Also the formula for L̄ is given.
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