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I know that $\int f(x) \overline{g(x)} dx$ is an inner product on $L^2$. But is it one on $L^1$? I think it isn't, but I am have had difficulty figuring out which defining property is violated.

Thanks in advance for any pointers!

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    Think about a real space and about $x^a$ for some appropriate $a$.2011-01-21

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