Characterizations of inner product spaces by means of norm one points

Authors

  • José Mendoza
  • Tijani Pakhrou

DOI:

https://doi.org/10.7146/math.scand.a-14966

Abstract

Let $X$ be a a real normed linear space of dimension at least three, with unit sphere $S_X$. In this paper we prove that $X$ is an inner product space if and only if every three point subset of $S_X$ has a Chebyshev center in its convex hull. We also give other characterizations expressed in terms of centers of three point subsets of $S_X$ only. We use in these characterizations Chebyshev centers as well as Fermat centers and $p$-centers.

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Published

2005-09-01

How to Cite

Mendoza, J., & Pakhrou, T. (2005). Characterizations of inner product spaces by means of norm one points. MATHEMATICA SCANDINAVICA, 97(1), 104–114. https://doi.org/10.7146/math.scand.a-14966

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Articles