Continuous functional calculus
= Continuous functional calculus
{title2=$f\mapsto f(a)$}
{wiki}
For a <Normal element of a C-star algebra> $a$ in a unital <C-star algebra>, the <Commutative Gelfand--Naimark theorem> identifies $C(\sigma(a))$ isometrically with the closed unital algebra generated by $a$ and $a^*$. The coordinate function maps to $a$, defining $f(a)$ for every continuous $f$ on the <spectrum of an element>.