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arXiv · 1905.13552

On some local Bishop-Phelps-Bollob\'as properties

Sheldon Dantas·Sun Kwang Kim·Han Ju Lee·Martin Mazzitelli
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Abstract

We continue a line of study about some local versions of Bishop-Phelps-Bollob\'as type properties for bounded linear operators. We introduce and focus our attention on two of these local properties, which we call L$_{p, o}$ and L$_{o, p}$, and we explore the relation between them and some geometric properties of the underlying spaces, such as spaces having strict convexity, local uniform rotundity, and property $\beta$ of Lindenstrauss. At the end of the paper, we present a diagram comparing all the existing Bishop-Phelps-Bollob\'as type properties with each other. Some open questions are left throughout the article.

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Sheldon Dantas, Sun Kwang Kim, Han Ju Lee, Martin Mazzitelli. 2019-05-31. On some local Bishop-Phelps-Bollob\'as properties. https://arxiv.org/abs/1905.13552

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