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

 

On the Dieudonné property for $ C(\Omega,E)$


Authors: N. J. Kalton, E. Saab and P. Saab
Journal: Proc. Amer. Math. Soc. 96 (1986), 50-52
MSC: Primary 46E40; Secondary 46B20, 46G99
MathSciNet review: 813808
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Abstract: In a recent paper, F. Bombal and P. Cembranos showed that if $ E$ is a Banach space such that $ {E^*}$ is separable, then $ C(\Omega ,E)C$, the Banach space of continuous functions from a compact Hausdorff space $ \Omega $ to $ E$, has the Dieudonné property. They asked whether or not the result is still true if one only assumes that $ E$ does not contain a copy of $ {l_1}$. In this paper we give a positive answer to their question. As a corollary we show that if $ E$ is a subspace of an order continuous Banach lattice, then $ E$ has the Dieudonné property if and only if $ C(\Omega ,E)$ has the same property.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0813808-8
PII: S 0002-9939(1986)0813808-8
Keywords: Dieudonné property
Article copyright: © Copyright 1986 American Mathematical Society