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Some questions about rotundity and renormings in Banach spaces

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

A. Aizpuru  and
F. J. Garcia-Pacheco
A. Aizpuru
Affiliation:
Departamento de Matem´ticasFacultad de CienciasUniversidad de C´dizPolígono Río San Pedro11.510 Puerto Real (C´diz)Spain e-mail: antonio.aizpuru@uca.es, fjavier.garcia@uca.es
F. J. Garcia-Pacheco
Affiliation:
Departamento de Matem´ticasFacultad de CienciasUniversidad de C´dizPolígono Río San Pedro11.510 Puerto Real (C´diz)Spain e-mail: antonio.aizpuru@uca.es, fjavier.garcia@uca.es
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Abstract

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In this paper, we show some results involving classical geometric concepts. For example, we characterize rotundity and Efimov-Stechkin property by mean of faces of the unit ball. Also, we prove that every almost locally uniformly rotund Banach space is locally uniformly rotund if its norm is Fréchet differentiable. Finally, we also provide some theorems in which we characterize the (strongly) exposed points of the unit ball using renormings.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 1 , August 2005 , pp. 131 - 140
Copyright
Copyright © Australian Mathematical Society 2005

References

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