The bidual of 𝐶(𝑋,𝐸)

Cambern, Michael; Greim, Peter

doi:10.1090/S0002-9939-1982-0647896-5

The bidual of $C(X, E)$
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by Michael Cambern and Peter Greim PDF

Proc. Amer. Math. Soc. 85 (1982), 53-58 Request permission

Abstract:

In this article we obtain, under certain conditions, a characterization of the bidual of the space $C(X,E)$ of continuous functions on a compact Hausdorff space $X$ to a Banach space $E$. It is shown that if $X$ is dispersed and $E$ is arbitrary, or if $X$ is arbitrary and ${E^* }$ has the Radon-Nikodym property, then $C{(X,E)^{**}}$ can be represented as a space of continuous functions on a compact Hausdorff space $Z$ to ${E^{**}}$ when the latter space is given its weak* topology.

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