English

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 f^\widehat{f} of a Lipschitz map f:MNf:M\to N is Dunford-Pettis if and only if it is Radon-Nikod\'ym if and only if it does not fix any copy of L1L_1. We also identify and study the corresponding metric property of ff, which is a natural extension of the curve-flatness.

Keywords

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

R2 v1 2026-06-28T19:57:59.549Z