= Maximal ideal space of a commutative Banach algebra
{title2=$\mathcal M_A\cong\Phi_A$}
= Maximal ideal space
{synonym}
For a commutative complex unital <Banach algebra>, <maximal ideals> correspond bijectively to <characters of an algebra> by taking kernels. Give the maximal ideal space the <Gelfand topology> through this correspondence. It is a <compact Hausdorff space>, since the characters form a weak-star closed subset of the dual unit ball, which is compact by the <Banach-Alaoglu theorem>.
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