## convergence of complex sequence

Let $\{ a_{n} \}$ be a complex sequence such that $\sum_{n=1}^{\infty} a_{n} b_{n}$ converges whenever $b_{n} \in l^2$.
Prove that $a_{n} \in l^2$.

( $b_{n} \in l^2$ means $\sum_{n=1}^{\infty} | b_{n}|^{2}$ converges. )