A submetric characterization of Rolewicz’s property $(\beta )$
Volume 265 / 2022
Studia Mathematica 265 (2022), 303-314 MSC: Primary 46B20; Secondary 46B80, 46B85. DOI: 10.4064/sm210319-9-10 Published online: 17 March 2022
The main result is a submetric characterization of the class of Banach spaces admitting an equivalent norm with Rolewicz’s property $(\beta )$. As applications we prove that up to renorming, property $(\beta )$ is stable under coarse Lipschitz embeddings and coarse quotients.