1. Let X be an inner product space. Using the parallelogram identity to prove by few...

 

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1. Let X be an inner product space. Using the parallelogram identity to prove by few lines the Appolonius' identity: |lz - x||2+||z– y||² = ||x – y|| + 2 2. Prove that the norm function f (x) ||x||:X R on a vector space X is continuous. %3D 1. Let X be an inner product space. Using the parallelogram identity to prove by few lines the Appolonius' identity: |lz - x||2+||z– y||² = ||x – y|| + 2 2. Prove that the norm function f (x) ||x||:X R on a vector space X is continuous. %3D