Asymptotically Convex Banach Spaces and The Index of Rotundity Problem

  • Francisco J. García-Pacheco University of Cadiz.
Palabras clave: Rotund, renorming, Banach space, rotonda, renormalización, espacio de Banach.

Resumen

The Index of Rotundity Problem asks whether a Banach space which admits equivalent renormings with index of rotundity as small as desired also admits an equivalent rotund renorming. In this paper we continue the ongoing search for a negative answer to this question by making use of a new concept: asymptotically convex Banach spaces. Some applications to The Approximation Hyperplane Series Property are given.

Biografía del autor/a

Francisco J. García-Pacheco, University of Cadiz.
Department of Mathematics.

Citas

[1] M.D. Acosta, R.M. Aron, D. García, and M. Maestre, The BishopPhelps-Bollobas Theorem for operators, J. Funct. Anal. 254 11, pp. 2780—2799, (2008).

[2] M.D. Acosta, R.M. Aron, F.J. García-Pacheco, Something rare is going on with the Approximation Hyperplane Series Property, Preprint.

[3] R. Deville, G. Godefroy and V. Zizler, Smoothness and renormings in Banach spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64, Longman Scientific, New York, (1993).

[4] J. Lindenstrauss, On operators which attain their norms, Israel J. Math. 1, pp. 139—148, (1963).
Publicado
2012-06-17
Cómo citar
García-Pacheco, F. (2012). Asymptotically Convex Banach Spaces and The Index of Rotundity Problem. Proyecciones. Revista De Matemática, 31(2), 91-101. https://doi.org/10.4067/S0716-09172012000200001
Sección
Artículos