convergence of complex sequence

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May 18th 2012, 04:56 AM
Cruella

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. )

Please help me.

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