By Lemma 1.15, we can find a sequence $\{\beta_{n}\}_{n=1}^{\infty}$ such that $|\beta_{n}|>1$ and $\lim_{n\to\infty}|\beta_{n}|=1$. On the other hand, by Lemma 1.16,

$$\|\raisebox{1.72218pt}{.}\|\leq\|\raisebox{1.72218pt}{.}\|_{\mathscr{V}}\leq|\beta_{n}|\|\raisebox{1.72218pt}{.}\|.$$

Therefore the assertion follows. ∎