Historical Remarks
One of Gelfand's original applications (and one which historically motivated much of the study of Banach algebras) 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 algebras L1(R) and whose translates span dense subspaces in the respective algebras.
Read more about this topic: Gelfand Representation
Famous quotes containing the words historical and/or remarks:
“After so many historical illustrations of the evil effects of abandoning the policy of protection for that of a revenue tariff, we are again confronted by the suggestion that the principle of protection shall be eliminated from our tariff legislation. Have we not had enough of such experiments?”
—Benjamin Harrison (1833–1901)
“I begin, then, with some remarks about ‘the meaning of a word.’ I think many persons now see all or part of what I shall say: but not all do, and there is a tendency to forget, or to get it slightly wrong. In so far as I am merely flogging the converted, I apologize to them.”
—J.L. (John Langshaw)