Under some mild assumptions, non-linear diameter-preserving bijections between (vector-valued) function spaces are characterized with the help of a well-known theorem of Ulam and Mazur. A necessary and sufficient condition for the existence of a diameter-preserving bijection between function spaces in the complex scalar case is derived, and a complete description of such maps is given in several important cases.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-3,
author = {Bruce A. Barnes and Ashoke K. Roy},
title = {Diameter-preserving maps on various classes of function spaces},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {127-145},
zbl = {1028.46053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-3}
}
Bruce A. Barnes; Ashoke K. Roy. Diameter-preserving maps on various classes of function spaces. Studia Mathematica, Tome 151 (2002) pp. 127-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-3/