Asymptotically Convex Banach Spaces and The Index of Rotundity Problem

• García-Pacheco, Francisco J. ^[1]
  1. [1] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 31, Nº. 2, 2012, págs. 91-101
• Idioma: inglés
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• 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.