The Mathematical Legacy of Victor Lomonosov: Operator Theory

초록

We continue a line of study initiated in [12, 16] about some local versions of Bishop-Phelps-Bollobás-type properties for bounded linear operators. We introduce and focus our attention on two of these local properties, which we call Lp,o and Lo,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 β of Lindenstrauss. At the end of the paper, we present a diagram comparing all the existing Bishop-Phelps-Bollobás type properties with each other. Some open questions are left throughout the article. © 2020 Walter de Gruyter GmbH, Berlin/Munich/Boston.