On the Composition of Differentiable Functions
Copyright policy )On the Composition of Differentiable Functions
AbstractWe 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 ○ 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.
- Pantheon-Sorbonne University France
- University of Bordeaux France
- University of Franche-Comté France
Geometry and structure of normed linear spaces, Differentiable maps on manifolds, Derivatives of functions in infinite-dimensional spaces, Fréchet differentiability, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, weak differentiability, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Schur poperty, 510
Geometry and structure of normed linear spaces, Differentiable maps on manifolds, Derivatives of functions in infinite-dimensional spaces, Fréchet differentiability, Differentiation theory (Gateaux, Fréchet, etc.) on manifolds, weak differentiability, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Schur poperty, 510
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