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-products – Arturo Magidin May 03 '11 at 17:00
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@Arturo: I've edited in your link. – t.b. May 03 '11 at 17:05