On some local Bishop-Phelps-Bollob\'as properties
Functional Analysis
2019-06-03 v1
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 and L, 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 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.
Cite
@article{arxiv.1905.13552,
title = {On some local Bishop-Phelps-Bollob\'as properties},
author = {Sheldon Dantas and Sun Kwang Kim and Han Ju Lee and Martin Mazzitelli},
journal= {arXiv preprint arXiv:1905.13552},
year = {2019}
}