A result of J.A. Goldstein extends Wiener's lemma from harmonic analysis about continuous and atomic measures to Hilbert space contractions. In this talk we discuss the relation between that lemma of Wiener and the Jacobs-de Leeuw-Glicksberg decomposition from operator theory. By using this decomposition we prove Goldstein's result in a way that is closer to the elementary proof of Wiener's lemma, and in a slightly stronger form at that. The presented proof appears to be new and worthy of mentioning.