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3.10 Show that a norm ||-|| on a linear space X is generated by a scalar product if and only if the parallelogram equality

3.10 Show that a norm ||-|| on a linear space X is generated by a scalar product if and only if the parallelogram equality ||x+y||+ ||xy|| = 2(||*|| + ||y||) holds for all x, y EX. Show that the and loo norms on C" are not generated by scalar products.

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