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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local dual spaces of Banach spaces of vector-valued functions


Authors: Manuel González and Antonio Martínez-Abejón
Journal: Proc. Amer. Math. Soc. 130 (2002), 3255-3258
MSC (2000): Primary 46B10, 46B20; Secondary 46B04, 46B08
Published electronically: April 22, 2002
MathSciNet review: 1913004
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Abstract: We show that $L_\infty(\mu,X^*)$ is a local dual of $L_1(\mu,X)$, and $L_1(\mu,X^*)$ is a local dual of $L_\infty(\mu,X)$, where $X$ is a Banach space. A local dual space of a Banach space $Y$ is a subspace $Z$ of $Y^*$ so that we have a local representation of $Y^*$ in $Z$ satisfying the properties of the representation of $X^{**}$ in $X$ provided by the principle of local reflexivity.


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Additional Information

Manuel González
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander, Spain
Email: gonzalem@unican.es

Antonio Martínez-Abejón
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, E-33007 Oviedo, Spain
Email: ama@pinon.ccu.uniovi.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06626-1
PII: S 0002-9939(02)06626-1
Keywords: Local dual space, local reflexivity, norming subspace, Banach spaces of vector-valued functions
Received by editor(s): June 5, 2001
Published electronically: April 22, 2002
Additional Notes: This work was supported in part by DGICYT Grant PB 97–0349
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society