Biblioteca de la Universidad Complutense de Madrid

Characterizations of inner product spaces by means of norm one points

Impacto



Mendoza Casas, José y 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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URL Oficial: http://www.mscand.dk/article.php?id=2869




Resumen

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.


Tipo de documento:Artículo
Palabras clave:Chebyshev centers; characterizations of inner product spaces
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:16864
Referencias:

Amir, D., Characterizations of Inner Product Spaces, Birkhäuser Verlag, Basel, 1986.

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Benítez, C., Fernández, M., and Soriano, L., Location of the Fermat-Torricelli medians of three points, Trans. Amer. Math. Soc. 304 (2002), 5027–5038.

Durier, R., Optimal locations and inner products, J. Math. Anal. Appl. 207 (1997), 220–239.

Garkavi, A. L., On the Chebyshev center and the convex hull of a set, Uspekhi Mat. Nauk USSR 19 (1964), 139–145.

Klee, V., Circumspheres and inner products, Math. Scand. 8 (1960), 363–370.

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

Depositado:25 Oct 2012 08:38
Última Modificación:07 Feb 2014 09:37

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