Let $x=(x_i)_{i=1}^{\infty}$ be a sequence such that for all $y=(y_i)_{i=1}^{\infty}$ $\in l^2(\mathbb{N})$
$\sum\limits_{k=0}^{\infty}|x_iy_i|< \infty $
Show that $x \in l^2(\mathbb{N})$ .
Can you please give some hint about solving this problem. I don't know even how to start it. Thanks !
