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. )

Please help me.