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Characterizations of inner product spaces by means of norm one points

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
References:

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Mendoza, J., and Pakhrou, T., On some characterizations of inner product spaces, J. Math. Anal. Appl. 282 (2003), 369–382.

Deposited On:25 Oct 2012 08:38
Last Modified:07 Feb 2014 09:37

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