A note on measures related to compactness and the Banach–Saks property in $$l_{1}$$

Abstract

AbstractUsing the Bessaga–Pełczyński selection principle, we give an alternative and concise proof of the results obtained by Tu (Arch Math, 117:315–322, 2021) that several quantities defined for bounded subsets of Banach spaces and related to compactness, weak compactness, and the Banach–Saks property coincide in $$l_{1}$$ l 1 .