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. )

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