On Hilbert extensions of Weierstrass' theorem with weights

Abstract

In this paper we study the set of functions \(\GG\)-valued which can be approximated by \(\GG\)-valued continuous functions in the norm \(L^\infty_{\GG}(I,w)\), where \(I\) is a compact interval, \(\GG\) is a real and separable Hilbert space and \(w\) is certain \(\GG\)-valued weakly measurable weight. Thus, we obtain a new extension of celebrated Weierstrass approximation theorem.