Let \(A\) be a C*-algebra, and consider the set of characters

\[\Omega(A) = \{ \chi : A \to \mathbb{C} : \chi\; \text{is a homomorphism} \}.\]

Then given an element \(a \in A\), we define the Gelfand transform of \(a\) as the element \(\hat{a} : \Omega(A) \to \mathbb{C}\) by

\[\hat{a}(\chi) = \chi(a).\]