The Gelfand representation is a powerful concept in the field of functional analysis and operator theory, specifically related to the study of commutative Banach algebras. Named after the mathematician Ilya Gelfand, the Gelfand representation provides a way to represent elements of a commutative Banach algebra as continuous functions on a compact Hausdorff space.
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For a unital commutative complex Banach algebra , the Gelfand transform sends to the continuous function on its character space of an algebra. It is a contractive unital algebra homomorphism into .