The bidual of $C(X, E)$
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- by Michael Cambern and Peter Greim
- Proc. Amer. Math. Soc. 85 (1982), 53-58
- DOI: https://doi.org/10.1090/S0002-9939-1982-0647896-5
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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.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 53-58
- MSC: Primary 46E40; Secondary 46B22
- DOI: https://doi.org/10.1090/S0002-9939-1982-0647896-5
- MathSciNet review: 647896