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Normed spaces and the parallelogram identity

  1. Jan 12, 2008 #1

    quasar987

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    1. The problem statement, all variables and given/known data
    My professor stated the theorem "If (X,<,>) is an an inner product space and || || is the norm generated by <,>, then we have ||x+y||² + ||x-y||² = 2(||x||² + ||y||²)." But then she also said that the converse was true. I suppose this means that "Given (X, || ||) a normed space, if it satisfies the parallelogram identity, then the norm is issued from an inner product."

    I do not have an idea as to how to prove that converse.
     
  2. jcsd
  3. Jan 12, 2008 #2

    morphism

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