Local dual spaces of Banach spaces of vector-valued functions
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- by Manuel González and Antonio Martínez-Abejón PDF
- Proc. Amer. Math. Soc. 130 (2002), 3255-3258 Request permission
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.References
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Additional Information
- Manuel González
- Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander, Spain
- MR Author ID: 219505
- 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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3255-3258
- MSC (2000): Primary 46B10, 46B20; Secondary 46B04, 46B08
- DOI: https://doi.org/10.1090/S0002-9939-02-06626-1
- MathSciNet review: 1913004