Which normed vector spaces satisfy the parallelogram law?: Encyclopedia II – Parallelogram law – Which normed vector spaces satisfy the parallelogram law?
Most real normed vector spaces do not have inner products, but all normed vector spaces have norms (hence the name), and thus one can evaluate the expressions on both sides of “=” in the identity above. A remarkable fact is that the identity above holds only if the norm is one that arises in the usual way from an inner product, because, if the identity above holds, then the function is an inner product whose norm is precisely this one. …
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- Which normed vector spaces satisfy the parallelogram law?: Encyclopedia II - Parallelogram law - Which normed vector spaces satisfy the parallelogram law?
- Which normed vector spaces satisfy the parallelogram law?
