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If $\sum a_n b_n <\infty$ for all $(b_n)\in \ell^2$ then $(a_n) \in \ell^2$
I have a question, can anyone help me?
Let $\{ a_i\} _{i=1} ^ { + \infty }$ be a sequence of positive real numbers such that for every sequence $\{ b_i\} _{i=1} ^ { + \infty }$ of positive real numbers satisfying the condition $\sum {b_n ^2} <+ \infty$ we have $\sum {a_n b_n} < + \infty$ . Prove that $\sum {a_n^2} < + \infty$.
It appeared in Iran's 3rd round Olympiad exam 2009, but I think it's a well-known result.