Summary
We investigate the possibility of representing a convex mapping f with values in some space C(T) of continuous functions on a compact space T, as a supremum of continuous affine mappings, when the domain D of f is some convex subset of a Banach space X. Various limiting examples are presented.
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Penot, J.P., Théra, M. Applications sous-linéaires à valeurs dans un espace de fonctions continues. Annali di Matematica pura ed applicata 136, 133–151 (1984). https://doi.org/10.1007/BF01773381
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DOI: https://doi.org/10.1007/BF01773381