We prove that every map T between two F*-spaces which preserves equality of distance and satisfies T(0) = 0 is linear.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-3-5, author = {Dongni Tan}, title = {On Maps which Preserve Equality of Distance in F*-spaces}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {56}, year = {2008}, pages = {225-230}, zbl = {1170.46301}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-3-5} }
Dongni Tan. On Maps which Preserve Equality of Distance in F*-spaces. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 225-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-3-5/