# A bounded sequence in $l^1$ which does not admit a weak convergent subsequence?

I saw several examples for bounded sequences in $L^1$ which do not admit a weak convergent subsequence. But what about $l^1$ the sequence space?

The canonical Schauder basis $(e_n)_{n=1}^\infty$ does not admit any weakly convergent subsequence.
By the way, observe that weakly convergent sequences in $\ell_1$, by the Schur property, are the same as norm convergent ones.