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:
“The analogy between the mind and a computer fails for many reasons. The brain is constructed by principles that assure diversity and degeneracy. Unlike a computer, it has no replicative memory. It is historical and value driven. It forms categories by internal criteria and by constraints acting at many scales, not by means of a syntactically constructed program. The world with which the brain interacts is not unequivocally made up of classical categories.”
—Gerald M. Edelman (b. 1928)
“I thought my razor was dull until I heard his speech and that reminds me of a story that’s so dirty I’m ashamed to think of it myself.”
—S.J. Perelman, U.S. screenwriter, Bert Kalmar, Harry Ruby, and Norman Z. McLeod. Groucho Marx, Horsefeathers, as a newly-appointed college president commenting on the remarks of Huxley College’s outgoing president (1932)