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Journal of Convex Analysis 24 (2017), No. 1, 333--347
Copyright Heldermann Verlag 2017

A Note on the Extension of Continuous Convex Functions from Subspaces

Carlo Alberto De Bernardi
Dip. di Matematica, UniversitÓ di Milano, Via C. Saldini 50, 20133 Milano, Italy


Let $Y$ be a subspace of a real normed space $X$. We say that the couple $(X,Y)$ has the {\em $\mathrm{CE}$-property} (``convex extension property'') if each continuous convex function on $Y$ admits a continuous convex extension defined on $X$. By using techniques of Johnson and Zippin, we prove the following results about the $\mathrm{CE}$-property: if $X$ is the $c_0(\Gamma)$-sum or the $\ell_p(\Gamma)$-sum ($1
Keywords: Convex function, extension, normed linear space.

MSC: 52A41; 26B25, 46A99

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