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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.

Information

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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