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A local approach to functionals on $L^{\infty }(\mu ,X)$


Author: Santiago Díaz
Journal: Proc. Amer. Math. Soc. 128 (2000), 101-109
MSC (1991): Primary 46E40
Published electronically: June 21, 1999
MathSciNet review: 1657715
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Abstract: Let $(\Omega ,\Sigma ,\mu )$ be a probability space and $X$ a Banach space. We show that the dual of $L^{\infty }(\mu ,X)$ can be ``locally'' identified with $L^{1}(\mu ,X^{*}).$


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Additional Information

Santiago Díaz
Affiliation: Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos 41092, Sevilla, Spain
Email: madrigal@cica.es

DOI: https://doi.org/10.1090/S0002-9939-99-05284-3
Keywords: Integrable functions, local reflexivity
Received by editor(s): March 6, 1998
Published electronically: June 21, 1999
Additional Notes: This research has been partially supported by the DGICYT project n. PB97-0706 and by La Consejería de Educación y Ciencia de la Junta de Andalucía.
Communicated by: Dale Alspach
Article copyright: © Copyright 1999 American Mathematical Society