It is known that if is a finite-dimensional Banach space, or a strictly convex space, or the space , then every nonexpansive bijection of its unit ball is an isometry. We extend these results to nonexpansive bijections between unit balls of two different Banach spaces. Namely, if is an arbitrary Banach space and is finite-dimensional or strictly convex, or the space , then every nonexpansive bijection is an isometry.
"Nonexpansive bijections between unit balls of Banach spaces." Ann. Funct. Anal. 9 (2) 271 - 281, May 2018. https://doi.org/10.1215/20088752-2017-0050