Abstract
We prove that, in every infinite dimensional Hilbert space, there exists $t_0>-1$ such that the smallest Lipscthiz constant of retractions from the unit ball onto its boundary is the same as the smallest Lipschitz constant of retractions from the unit ball onto its $t$-spherical cup for all $t\in[-1,t_0]$.
Citation
Jumpot Intrakul. Phichet Chaoha. Wacharin Wichiramala. "Lipschitz retractions onto sphere vs spherical cup in a Hilbert space." Topol. Methods Nonlinear Anal. 52 (2) 677 - 691, 2018. https://doi.org/10.12775/TMNA.2018.034