On the Dieudonné property for 𝐶(Ω,𝐸)

Kalton, N. J.; Saab, E.; Saab, P.

doi:10.1090/S0002-9939-1986-0813808-8

On the Dieudonné property for $C(\Omega ,E)$
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by N. J. Kalton, E. Saab and P. Saab PDF

Proc. Amer. Math. Soc. 96 (1986), 50-52 Request permission

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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