Exercise 17, § 3

Let $A$ be a commutative Banach algebra and $I$ a closed ideal of $A$. Denote by $h$ the canonical injection of $I$ into $A$. The space $\mathsf{X}'(I)$ is identified with the quotient space of $\mathsf{X}'(A)$ by the equivalence relation defined by $\mathsf{X}'(h)$. (Use part a) of Exercise 4 of I, p. 153).