Asymptotically Convex Banach Spaces and The Index of Rotundity Problem

Francisco J. García-Pacheco

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.

Palabras clave


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

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Referencias


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).

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

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).

J. Lindenstrauss, On operators which attain their norms, Israel J. Math. 1, pp. 139—148, (1963).




DOI: http://dx.doi.org/10.4067/S0716-09172012000200001

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