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Journal Articles North-Western European Journal of Mathematics Year : 2017

Limited operators and differentiability

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Mohammed Bachir
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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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Dates and versions

hal-01488651 , version 1 (13-03-2017)

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  • HAL Id : hal-01488651 , version 1

Cite

Mohammed Bachir. Limited operators and differentiability. North-Western European Journal of Mathematics, 2017. ⟨hal-01488651⟩
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