On curve-flat Lipschitz functions and their linearizations

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 $\hat{f}$ of a Lipschitz map $f:M\to N$ is Dunford-Pettis if and only if it is Radon-Nikodým 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.

33 pages