Limited operators and differentiability

Mohammed Bachir

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arXiv · 1602.04173

Limited operators and differentiability

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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Mohammed Bachir. 2016-02-12. Limited operators and differentiability. https://arxiv.org/abs/1602.04173

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