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/