We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
@article{bwmeta1.element.bwnjournal-article-zmv25i3p381bwm,
author = {E. Ignaczak and A. Paszkiewicz},
title = {Extensions of convex functionals on convex cones},
journal = {Applicationes Mathematicae},
volume = {25},
year = {1998},
pages = {381-386},
zbl = {0995.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv25i3p381bwm}
}
Ignaczak, E.; Paszkiewicz, A. Extensions of convex functionals on convex cones. Applicationes Mathematicae, Tome 25 (1998) pp. 381-386. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv25i3p381bwm/
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