Some remarks on almost locally uniformly rotund points
Functional Analysis
2026-04-20 v2
Abstract
We study the relations between different notions of almost locally uniformly rotund points that appear in literature. We show that every non-reflexive Banach space admits an equivalent norm having a point in the corresponding unit sphere which is not almost locally uniformly rotund, and which is strongly exposed by all its supporting functionals. This result is in contrast with a characterization due to P. Bandyopadhyay, D. Huang, and B.-L. Lin from 2004. We also show that such a characterization remains true in reflexive Banach spaces.
Cite
@article{arxiv.2504.04848,
title = {Some remarks on almost locally uniformly rotund points},
author = {Carlo Alberto De Bernardi and Jacopo Somaglia},
journal= {arXiv preprint arXiv:2504.04848},
year = {2026}
}