Characterizing of Inner Product Spaces by the Mapping $n_{x,y}$

Hossein Dehghan

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arXiv · 1502.02250

Characterizing of Inner Product Spaces by the Mapping $n_{x,y}$

Hossein Dehghan

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Abstract

For the vectors $x$ and $y$ in a normed linear spaces $X$, the mapping $n_{x,y}: \mathbb{R}\to \mathbb{R}$ is defined by $n_{x,y}(t)=\|x+ty\|$. In this note, comparing the mappings $n_{x,y}$ and $n_{y,x}$ we obtain a simple and useful characterization of inner product spaces.

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Hossein Dehghan. 2015-02-08. Characterizing of Inner Product Spaces by the Mapping $n_{x,y}$. https://arxiv.org/abs/1502.02250

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