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:
“What are your historical Facts; still more your biographical? Wilt thou know a Man ... by stringing-together beadrolls of what thou namest Facts?”
—Thomas Carlyle (1795–1881)
“An illustrious individual remarks that Mrs. [Elizabeth Cady] Stanton is the salt, Anna Dickinson the pepper, and Miss [Susan B.] Anthony the vinegar of the Female Suffrage movement. The very elements get the “white male” into a nice pickle.”
—Anonymous, U.S. women’s magazine contributor. The Revolution (August 19, 1869)