# Limited operators and differentiability

* 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 $T(y)\in X$.
Keywords :
Document type :
Preprints, Working Papers, ...

Cited literature [12 references]

https://hal-paris1.archives-ouvertes.fr/hal-01265147
Contributor : Mohammed Bachir <>
Submitted on : Friday, February 12, 2016 - 11:12:06 AM
Last modification on : Monday, November 27, 2017 - 2:14:02 PM
Long-term archiving on : Saturday, November 12, 2016 - 7:22:37 PM

### Files

LIMITED-OPERATOR.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01265147, version 2
• ARXIV : 1602.04173

### Citation

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

Record views