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)
“Where do whites fit in the New Africa? Nowhere, I’m inclined to say ... and I do believe that it is true that even the gentlest and most westernised Africans would like the emotional idea of the continent entirely without the complication of the presence of the white man for a generation or two. But nowhere, as an answer for us whites, is in the same category as remarks like What’s the use of living? in the face of the threat of atomic radiation. We are living; we are in Africa.”
—Nadine Gordimer (b. 1923)