I would like to know,
Why is it true that $e_n$, the nth unit vector in $\ell^p(\mathbb N)$ converges weakly to $0$. $1 < p < \infty$ According to Mazur's lemma, which says that $y_n$ is convex combination of $e_n$ converges to $0$ in norm topology. I am trying to construct an explicit convex combination but i failed.
How do i construct it, any example would be nice. Thanks.