Asymptotically Convex Banach Spaces and The Index of Rotundity Problem

Francisco J. García-Pacheco


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.

Palabras clave

Rotund; renorming; Banach space; rotonda; renormalización; espacio de Banach.

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