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
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.
|Uncontrolled Keywords:||Chebyshev centers; characterizations of inner product spaces|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
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|Deposited On:||25 Oct 2012 10:38|
|Last Modified:||13 Nov 2013 17:30|
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