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## Limited operators and differentiability

Mohammed Bachir
• Function : Correspondent author
• PersonId : 960537

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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 $T(y)\in X$.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-01265147 , version 1 (31-01-2016)
hal-01265147 , version 2 (12-02-2016)

### Identifiers

• HAL Id : hal-01265147 , version 2
• ARXIV :

### Cite

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

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