We show how Kirszbraun's theorem on extending Lipschitz mappings in Hilbert space implies its own generalization. There is a continuous extension operator preserving the Lipschitz constant of every mapping.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-1-2,
author = {Eva Kopeck\'a},
title = {Bootstrapping Kirszbraun's extension theorem},
journal = {Fundamenta Mathematicae},
volume = {219},
year = {2012},
pages = {13-19},
zbl = {1244.54040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-1-2}
}
Eva Kopecká. Bootstrapping Kirszbraun's extension theorem. Fundamenta Mathematicae, Tome 219 (2012) pp. 13-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm217-1-2/