Extensions of Continuous and Lipschitz Functions
Canadian mathematical bulletin, Tome 43 (2000) no. 2, pp. 208-217
Voir la notice de l'article provenant de la source Cambridge
We show a result slightly more general than the following. Let $K$ be a compact Hausdorff space, $F$ a closed subset of $K$ , and $d$ a lower semi-continuous metric on $K$ . Then each continuous function $f$ on $F$ which is Lipschitz in $d$ admits a continuous extension on $K$ which is Lipschitz in $d$ . The extension has the same supremum norm and the same Lipschitz constant.As a corollary we get that a Banach space $X$ is reflexive if and only if each bounded, weakly continuous and norm Lipschitz function defined on a weakly closed subset of $X$ admits a weakly continuous, norm Lipschitz extension defined on the entire space $X$ .
Mots-clés :
54C20, 46B10, extension, continuous, Lipschitz, Banach space
Matoušková, Eva. Extensions of Continuous and Lipschitz Functions. Canadian mathematical bulletin, Tome 43 (2000) no. 2, pp. 208-217. doi: 10.4153/CMB-2000-028-0
@article{10_4153_CMB_2000_028_0,
author = {Matou\v{s}kov\'a, Eva},
title = {Extensions of {Continuous} and {Lipschitz} {Functions}},
journal = {Canadian mathematical bulletin},
pages = {208--217},
year = {2000},
volume = {43},
number = {2},
doi = {10.4153/CMB-2000-028-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-028-0/}
}
Cité par Sources :