Let
Chapter 6, Problem 30(choose chapter or problem)
Let || || be a norm (as defined in Exercise 24) on a complex vector space V satisfying the parallelogram law given in Exercise 11. Prove that there is an inner product (, ) on V such that ||aj|| = (x,x) for all x G V. Hint: Apply Exercise 27 to V regarded as a vector space over R. Then apply Exercise 29.
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