Asymptotically Convex Banach Spaces and The Index of Rotundity Problem

  1. García-Pacheco, Francisco J. 1
  1. 1 University of Cadiz.
Revista:
Proyecciones: Journal of Mathematics

ISSN: 0716-0917,  0717-6279

Año de publicación: 2012

Volumen: 31

Número: 2

Páginas: 91-101

Tipo: Artículo

DOI: 10.4067/S0716-09172012000200001 DIALNET GOOGLE SCHOLAR

Otras publicaciones en: Proyecciones: Journal of Mathematics

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.

Referencias bibliográficas

  • 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).
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