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ULTRAPOWERS AND SUBSPACES OF THE DUAL OF A BANACH SPACE

Published online by Cambridge University Press:  10 September 2003

MANUEL GONZÁLEZ  and
ANTONIO MARTÍNEZ-ABEJÓN
MANUEL GONZÁLEZ
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander (Spain) e-mail: gonzalem@unican.es
ANTONIO MARTÍNEZ-ABEJÓN
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, E-33007 Oviedo (Spain) e-mail: ama@pinon.ccu.uniovi.es
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Abstract

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For a Banach space $X$ we consider three ways in which a subspace of $X^*$ can represent locally the whole dual space $X^*$. We obtain characterizations in terms of ultrapowers and we study the relationship between the subspaces of $X^*$ and the subspaces of the dual of an ultrapower of $X$.

Keywords

Primary: 46B0846B10Secondary: 46B0446B20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 3 , September 2003 , pp. 493 - 501
Copyright
© 2003 Glasgow Mathematical Journal Trust

Footnotes

Supported in part by D.G.I. (Spain) Proyecto BFM2001-1147.