Using 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
.
Using 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
.
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