Bishop-Phelps-Bollob\'as property for positive operators when the domain is $C_0(L) $
| Autor: | Acosta, María D., Soleimani-Mourchehkhorti, Maryam |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Recently it was introduced the so-called Bishop-Phelps-Bollob{\'a}s property for positive operators between Banach lattices. In this paper we prove that the pair $(C_0(L), Y) $ has the Bishop-Phelps--Bollob{\'a}s property for positive operators, for any locally compact Hausdorff topological space $L$, whenever $Y$ is a uniformly monotone Banach lattice with a weak unit. In case that the space $C_0(L)$ is separable, the same statement holds for any uniformly monotone Banach lattice $Y .$ We also show the following partial converse of the main result. In case that $Y$ is a strictly monotone Banach lattice, $L$ is a locally compact Hausdorff topological space that contains at least two elements and the pair $(C_0(L), Y )$ has the Bishop-Phelps--Bollob{\'a}s property for positive operators then $Y$ is uniformly monotone. Comment: 9 pages. arXiv admin note: substantial text overlap with arXiv:1907.08620 |
| Databáze: | arXiv |
| Externí odkaz: |
|