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Characterizations of inner product spaces by means of norm one points

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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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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
Uncontrolled Keywords:Chebyshev centers; characterizations of inner product spaces
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16864
Deposited On:25 Oct 2012 08:38
Last Modified:26 Jul 2018 07:05

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