On curve-flat Lipschitz functions and their linearizations
Functional Analysis
2025-11-03 v2 Metric Geometry
Abstract
We show that several operator ideals coincide when intersected with the class of linearizations of Lipschitz maps. In particular, we show that the linearization of a Lipschitz map is Dunford-Pettis if and only if it is Radon-Nikod\'ym if and only if it does not fix any copy of . We also identify and study the corresponding metric property of , which is a natural extension of the curve-flatness.
Cite
@article{arxiv.2411.08369,
title = {On curve-flat Lipschitz functions and their linearizations},
author = {Gonzalo Flores and Mingu Jung and Gilles Lancien and Colin Petitjean and Antonín Procházka and Andrés Quilis},
journal= {arXiv preprint arXiv:2411.08369},
year = {2025}
}
Comments
33 pages