On Hilbert extensions of Weierstrass' theorem with weights (Q989238)

Summary: We study the set of \(\mathcal G \)-valued functions which can be approximated by \(\mathcal G \)-valued continuous functions in the norm \(L^{\infty }_{\mathcal G}(I,w)\), where \(I \subset R\) is a compact interval, \(\mathcal G\) is a separable real Hilbert space and \(w\) is a certain \(\mathcal G \)-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem.