# 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 $T(y)\in X$.
Keywords :
Document type :
Journal articles

https://hal-paris1.archives-ouvertes.fr/hal-01488651
Contributor : Mohammed Bachir <>
Submitted on : Monday, March 13, 2017 - 9:33:04 PM
Last modification on : Tuesday, January 19, 2021 - 11:08:56 AM

### Identifiers

• 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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