Example 3

Let Δ be the disk of complex numbers $z$ satisfying $|z|\leqslant 1$ and let A be the complex Banach algebra of continuous functions on Δ analytic in the interior of Δ, endowed with the norm $\|f\|=$ sup$_{z\in\Delta}|f(z)|$ (example 9 of I, p. 20). Then $\mathsf{X}(A)$ is identified with Δ and $\mathscr{G}$ with the inclusion of A in $\mathscr{C}(\Delta )$ (cf. Exercise 6 of I, p. 193).