Editing Gelfand representation (section)

{{Short description|Mathematical representation in functional analysis}}
In [[mathematics]], the '''Gelfand representation''' in [[functional analysis]] (named after [[I. M. Gelfand]]) is either of two things:

* a way of representing [[commutative]] [[Banach algebra]]s as algebras of continuous functions;
* the fact that for commutative [[C*-algebra]]s, 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 operator]]s, and generalizes the notion of diagonalizing a [[normal matrix]].