Exercise 18, § 1

Let E be a complex Hilbert space and let $I_E$ be the set defined in the n$^o3$ of IV, p. 151.

Let $n\in I_E$. Let F be a complex Hilbert space. The mapping $u\mapsto \lambda_n(|u|)$ of $\mathscr{L}^c(E; F)$ into $\mathbf{R}_+$ is continuous.