Editing Gelfand representation (section)

== Historical remarks ==
One of Gelfand's original applications (and one which historically motivated much of the study of Banach algebras{{Citation needed|date=December 2011}}) was to give a much shorter and more conceptual proof of a celebrated lemma of [[Norbert Wiener]] (see the citation below), characterizing the elements of the [[group algebra of a locally compact group|group algebra]]s ''L''<sup>1</sup>('''R''') and <math>\ell^1({\mathbf Z})</math> whose translates span dense subspaces in the respective algebras.