Eine Parallelogrammungleichung zum Exponenten $\gamma \in [1,2]$ für Normen

Abstract

For a Hilbert space $X$ the generalized parallelogramm inequality to the exponent $\gamma$

for every $x_1,x_2\in X,\lambda \in [0,1],\gamma \in [1,2]$ is proved and the constant $C(\gamma )$ is determined. The extension of this inequality to certain normed spaces is possible with restrictions of the parameter $\gamma$.