Geodesic
On the Composition of Differentiable Functions
Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 481-494

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DOI

We prove that a Banach space $X$ has the Schur property if and only if every $X$ -valued weakly differentiable function is Fréchet differentiable. We give a general result on the Fréchet 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 ${{\left\| {} \right\|}_{\text{lip}}}$ on various spaces of Lipschitz functions.
DOI : 10.4153/CMB-2003-047-2
Mots-clés : 58C20, 46B20 
Bachir, M.; Lancien, G. On the Composition of Differentiable Functions. Canadian mathematical bulletin, Tome 46 (2003) no. 4, pp. 481-494. doi: 10.4153/CMB-2003-047-2
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     title = {On the {Composition} of {Differentiable} {Functions}},
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     year = {2003},
     volume = {46},
     number = {4},
     doi = {10.4153/CMB-2003-047-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-047-2/}
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