We denote $\| u \| = \sup _ { \substack { x \in E \\ x \neq 0 } } \frac { \| u ( x ) \| } { \| x \| }$. Show that $\|.\|$ is a norm on $\mathcal { L } ( E )$.
We denote $\| u \| = \sup _ { \substack { x \in E \\ x \neq 0 } } \frac { \| u ( x ) \| } { \| x \| }$. Show that $\|.\|$ is a norm on $\mathcal { L } ( E )$.