]} \coloneqq \biggl\{f=(f_n)_{n=0}^{\infty}: f_n \in \mathbb{R} \ \text{for all} \   n \in \mathbb{N} \ \text{and} \   \sum\limits_{n=0}^{\infty} n|f_n|<\infty\biggr\}.$$ Equipped with the norm $$\label{