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Limited operators and differentiability

Mohammed Bachir 1
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 : 49J50 58C20 47B07
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Contributor : Mohammed Bachir <>
Submitted on : Monday, March 13, 2017 - 9:33:04 PM
Last modification on : Sunday, January 19, 2020 - 6:38:38 PM


  • HAL Id : hal-01488651, version 1



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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