On uniform and coarse rigidity of
Volume 268 / 2023
Studia Mathematica 268 (2023), 235-240
MSC: Primary 46B80; Secondary 46B20.
DOI: 10.4064/sm220603-6-8
Published online: 20 September 2022
Abstract
If X is an almost transitive Banach space with amenable isometry group (for example, if X=L^p([0,1]) with 1\leq p \lt \infty ) and X admits a uniformly continuous map X\overset \phi \longrightarrow E into a Banach space E satisfying \inf _{\|x-y\|=r}\|\phi (x)-\phi (y)\| \gt 0 for some r \gt 0 (that is, \phi is almost uncollapsed), then X admits a simultaneously uniform and coarse embedding into a Banach space V that is finitely representable in L^2(E).
