Asymptotically Convex Banach Spaces and The Index of Rotundity Problem
DOI:
https://doi.org/10.4067/S0716-09172012000200001Keywords:
Rotund, renorming, Banach space, rotonda, renormalización, espacio de Banach.Abstract
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.References
[1] M.D. Acosta, R.M. Aron, D. García, and M. Maestre, The Bishop-Phelps-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).
[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).
Published
2012-06-17
How to Cite
[1]
F. J. García-Pacheco, “Asymptotically Convex Banach Spaces and The Index of Rotundity Problem”, Proyecciones (Antofagasta, On line), vol. 31, no. 2, pp. 91-101, Jun. 2012.
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