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arXiv · 2411.08369

On curve-flat Lipschitz functions and their linearizations

Gonzalo Flores·Mingu Jung·Gilles Lancien·Colin Petitjean·Antonín Procházka·Andrés Quilis
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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 $\widehat{f}$ of a Lipschitz map $f:M\to N$ is Dunford-Pettis if and only if it is Radon-Nikod\'ym if and only if it does not fix any copy of $L_1$. We also identify and study the corresponding metric property of $f$, which is a natural extension of the curve-flatness.

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Gonzalo Flores, Mingu Jung, Gilles Lancien, Colin Petitjean, Antonín Procházka, Andrés Quilis. 2024-11-13. On curve-flat Lipschitz functions and their linearizations. https://arxiv.org/abs/2411.08369

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