Mendoza Casas, José and Pakhrou, Tijani
(2005)
*Characterizations of inner product spaces by means of norm one points.*
Mathematica Scandinavica, 97
(1).
pp. 104-114.
ISSN 0025-5521

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Official URL: http://www.mscand.dk/article.php?id=2869

## 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.

Item Type: | Article |
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Uncontrolled Keywords: | Chebyshev centers; characterizations of inner product spaces |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 16864 |

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Deposited On: | 25 Oct 2012 08:38 |

Last Modified: | 07 Feb 2014 09:37 |

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