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Journal Articles Canad. Math. Bull Year : 2003

## On the Composition of Differentiable Functions

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Mohammed Bachir
• Function : Author
• PersonId : 960537
Gilles Lancien
• Function : Author
• PersonId : 856995

#### 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.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-01183277 , version 1 (07-08-2015)

### Identifiers

• HAL Id : hal-01183277 , version 1

### Cite

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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