# On the Composition of Differentiable Functions

1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : We prove that a Banach space $X$ has the Schur property if and only if every $X$-valued weakly differentiable function is Fr´echet differentiable. We give a general result on the Fr´echet differentiability of $f \circ T$, where $f$ is a Lipschitz function and $T$ is a compact linear operator. Finally we study, using in particular a smooth variational principle, the differentiability of the semi norm $\|.\|_{lip}$ on various spaces of Lipschitz functions.
Document type :
Journal articles

https://hal-paris1.archives-ouvertes.fr/hal-01183277
Contributor : Mohammed Bachir <>
Submitted on : Friday, August 7, 2015 - 12:02:42 AM
Last modification on : Tuesday, January 19, 2021 - 11:08:54 AM

### Identifiers

• HAL Id : hal-01183277, version 1

### Citation

Mohammed Bachir, Gilles Lancien. On the Composition of Differentiable Functions. Canad. Math. Bull, 2003, 46 (4), pp.481-494. ⟨hal-01183277⟩

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