Definition 2.24 . [00HV]

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Definition 2.24.

The Gelfand transform of $\mathcal{A}$ is the homomorphism of Banach $k$ -algebras

\widehat{}:A\to\prod_{z\in\mathfrak{M}(\mathcal{A})}\hat{\kappa}(z),\quad f\mapsto\widehat{f}=(f(z))_{z\in\mathfrak{M}(\mathcal{A})}