Lemma 2

Let $c$ be a real number. If $c <((u))$, then for every element $z\in$ Im($u$), there exists an element $x$ of E such that $u(x) =z$ and $c\|x\|\leqslant \|z\|$. Conversely, if for every $z\in$ Im($u$) there exists $x\in E$ such that $u(x) =z$ and $c\|x\|\leqslant \|z\|$, then $c\leqslant ((u))$.

This is a consequence of formulas (2) and (5) and of the definition of the conorm of $u$.