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

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

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