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Possible Duplicates:
Norms Induced by Inner Products
From norm to scalar product

Given a normed space $(X, \|\cdot\|)$. Is it possible to define an inner product $\langle \cdot, \cdot \rangle$ on space $X$ based on the norm $\|\cdot\|$?

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    A better fit, including a sketch of the proof, is in http://math.stackexchange.com/questions/21792/norms-induced-by-inner-products2011-05-03
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    @Arturo: I've edited in your link.2011-05-03

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