Proposition 3

Let A be a commutative regular Banach algebra, I an ideal of A and K a compact subset of $\mathsf{X}(A)$ disjoint from V(I). There exists an element $x\in I$ such that $\mathscr{G}(x) = 1$ for every $x$ in K.

This is a special case of prop. 15 of I, p. 81 taking into account the fact that the Jacobson topology coincides with the weak topology on $\mathsf{X}(A)$.