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Mathematik-Online problems:

Problem 455: Proof of the Parallelogram Law

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Show, that the parallelogram law

$\displaystyle \vert x+y \vert ^{2} + \vert x-y \vert ^{2}= 2 \vert x \vert ^{2} + 2 \vert y \vert ^{2} $

holds for a norm induced by a scalar product.

Is this true for the maximum norm, too? What implication does this allow?

(Author: unknown)
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  automatisch erstellt am 12.  3. 2018