I tried using the definition of absolute convergence (similar to Cauchy Criterion), but had trouble reaching at ajbj.
Any help would be greatly appreciated.
Thanks
i wasn't actually talking about that kind of application, what i meant is $\displaystyle \sum\limits_{j=1}^{\infty }{a_{j}b_{j}}\le \sqrt{\sum\limits_{j=1}^{\infty }{a_{j}^{2}}\cdot \sum\limits_{j=1}^{\infty }{b_{j}^{2}}}.$
(ohhh, may be it's the same, it's just that i'm not so familiar with norms.)