Remark

Let $u$ be a partial operator on E. Every endomorphism $v\in \mathscr{L}(E)$ is bounded relatively to $u$ and its relative norm is zero, since $\|v(x)\|\leqslant \|v\| \|x\|$ for every $x\in$ dom($u$), which makes it possible to take $a= 0$ in the above inequality.