Normed spaces and the parallelogram identity

1. Jan 12, 2008

quasar987

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. Jan 12, 2008

morphism

Last edited by a moderator: May 3, 2017