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In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) has two related meanings: * a way of representing commutative Banach algebras as algebras of continuous functions; * the fact that for commutative C *-algebras, this representation is an isometric isomorphism. In the former case, one may regard the Gelfand representation as a far-reaching generalization of the Fourier transform of an integrable function. In the latter case, the Gelfand-Naimark representation theorem is one avenue in the development of spectral theory for normal operators, and generalizes the notion of diagonalizing a normal matrix. == 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 ''L''1(R) and whose translates span dense subspaces in the respective algebras. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gelfand representation」の詳細全文を読む スポンサード リンク
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