# Limited operators and differentiability

1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : We characterize the limited operators by differentiability of convex continuous functions. Given Banach spaces $Y$ and $X$ and a linear continuous operator $T: Y \longrightarrow X$, we prove that $T$ is a limited operator if and only if, for every convex continuous function $f: X \longrightarrow \R$ and every point $y\in Y$, $f\circ T$ is Fr\'echet differentiable at $y\in Y$ whenever $f$ is G\^ateaux differentiable at $T(y)\in X$.
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Article dans une revue
North-Western European Journal of Mathematics, Laboratoires de Mathématiques du Nord-Pas-de-Calais, 2017

https://hal-paris1.archives-ouvertes.fr/hal-01488651
Contributeur : Mohammed Bachir <>
Soumis le : lundi 13 mars 2017 - 21:33:04
Dernière modification le : mardi 17 juillet 2018 - 15:49:05

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• HAL Id : hal-01488651, version 1

### Citation

Mohammed Bachir. Limited operators and differentiability. North-Western European Journal of Mathematics, Laboratoires de Mathématiques du Nord-Pas-de-Calais, 2017. 〈hal-01488651〉

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