Commutative Gelfand--Naimark theorem
= Commutative Gelfand--Naimark theorem
{c}
Every commutative unital C-star algebra $A$ is isometrically star-isomorphic to $C(\Phi_A)$ through its <Gelfand transform>, where $\Phi_A$ is its <character space of an algebra>. Thus abstract algebra elements can be treated as continuous functions on a compact Hausdorff space.
This is the isometric commutative C-star specialization of the <Gelfand representation>.