Year: 2025
Type: article
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–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.
DOI: 10.1093/imrn/rnaf132
Institutions: University of O'Higgins, Korea Institute for Advanced Study, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques de Besançon, Université Marie et Louis Pasteur, Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées, University of Tartu
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404407520