Limited operators and differentiability

Mohammed Bachir 1, *
* Corresponding author
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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Submitted on : Friday, February 12, 2016 - 11:12:06 AM
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  • HAL Id : hal-01265147, version 2
  • ARXIV : 1602.04173

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Mohammed Bachir. Limited operators and differentiability. 2016. ⟨hal-01265147v2⟩

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