Each operator in ${\cal L}(l^p,l^r)\ (1\leq r
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It is known that each bounded operator from $l^p\rightarrow l^r$ is compact. The purpose of this paper is to present a very simple proof of this useful fact.
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Grzaslewicz, R. (Ryszard). “Each operator in ${\cal L}(l^p,l^r)\ (1\leq r<p<\infty)$ is compact”. Collectanea Mathematica, vol.VOL 48, no. 4, pp. 539-41, https://raco.cat/index.php/CollectaneaMathematica/article/view/56410.