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 $\widehat{f}$ 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.
Authors
- A. Procházka (ORCID: https://orcid.org/0000-0001-7762-9147)
- Colin Petitjean (ORCID: https://orcid.org/0000-0002-6584-5405)
- Andrés Quilis (ORCID: https://orcid.org/0000-0001-6022-9286)
- Mingu Jung (ORCID: https://orcid.org/0000-0003-2240-2855)
- Gonzalo Flores (ORCID: https://orcid.org/0000-0001-6323-3766)
- Gilles Lancien
Institutions
- Korea Institute for Advanced Study (KR)
- Centre National de la Recherche Scientifique (FR)
- Université Paris-Est Créteil (FR)
- University of O'Higgins (CL)
- Laboratoire d’Analyse et de Mathématiques Appliquées (FR)
- Université Gustave Eiffel (FR)
- Université Marie et Louis Pasteur (FR)
- University of Tartu (EE)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-05-26
- DOI
- https://doi.org/10.1093/imrn/rnaf132
- Primary Topic
- Advanced Banach Space Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Centre National de la Recherche Scientifique
- Agencia Estatal de Investigación