On Hilbert extensions of Weierstrass′ theorem with weights

Abstract

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