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On denseness of certain norms in Banach spaces

Published online by Cambridge University Press:  17 April 2009

M. Jiménez Sevilla  and
J.P. Moreno
M. Jiménez Sevilla
Affiliation:
Departamento de Analisis Matematico, Facultad de Matematicas, Universidad Complutense de Madrid, Madrid 28040, Spain e-mail: marjim@sunaml.mat.ucm.esmoreno@sunaml.mat.ucm.es
J.P. Moreno
Affiliation:
Departamento de Analisis Matematico, Facultad de Matematicas, Universidad Complutense de Madrid, Madrid 28040, Spain e-mail: marjim@sunaml.mat.ucm.esmoreno@sunaml.mat.ucm.es
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Abstract

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We give several results dealing with denseness of certain classes of norms with many vertex points. We prove that, in Banach spaces with the Mazur or the weak* Mazur intersection property, every ball (convex body) can be uniformly approximated by balls (convex bodies) being the closed convex hull of their strongly vertex points. We also prove that given a countable set F, every norm can be uniformly approximated by norms which are locally linear at each point of F.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 183 - 196
Copyright
Copyright © Australian Mathematical Society 1996

References

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