Fréchet-valued pointwise Lipschitz maps (Q2906223)
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scientific article; zbMATH DE number 6077259
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fréchet-valued pointwise Lipschitz maps |
scientific article; zbMATH DE number 6077259 |
Statements
5 September 2012
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differentiability of pointwise Lipschitz maps
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super reflexive Fréchet space
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Fréchet-valued pointwise Lipschitz maps (English)
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Let \(Y\) be a super reflexive Fréchet space. It is proved that every map \(f:{\mathbb{R}}\longrightarrow Y\) has a derivative at almost each point at which \(f\) is pointwise Lipschitz. This result is an extension of a Phillips' theorem (1940) for Lipschitz maps from \({\mathbb{R}}\) into a reflexive Banach space.
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