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arXiv · 2504.04848

Some remarks on almost locally uniformly rotund points

Carlo Alberto De Bernardi·Jacopo Somaglia
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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.

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Carlo Alberto De Bernardi, Jacopo Somaglia. 2025-04-07. Some remarks on almost locally uniformly rotund points. https://arxiv.org/abs/2504.04848

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