Limited operators and differentiability
Résumé
Given Banach spaces Y and X and a linear continuous operator T : Y −→ X, we prove that T is a limited operator if and only if, for every convex continuous function f : X −→ R and every point y ∈ Y , f • T is Fréchet-differentiable at y ∈ Y whenever f is Gâteaux-differentiable at T (y) ∈ X. Some consequences will be given.
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