Exercise 15, § 2

Let $A =\mathbf{C}\cdot 1$. (If $x\in A$, and if $\lambda$ belongs to the boundary of Sp$_{\widehat{A}}(x)$, then $x-\lambda$ is a topological zero divisor in $\widehat{A}$, hence in A, hence $x=\lambda .$)