Exercise 2, § 4

Let $p\in [1,+\infty ]$, and $E =\ell^p_{\mathbf{C}}(\mathbf{N})$. Let $u$ be a diagonal endomorphism of E. For every $\lambda \in \mathbf{C}$, calculate $((u-\lambda 1_E))$ as a function of the spectrum of $u$.