On norm-attaining positive operators between Banach lattices
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909672621998080 |
|---|---|
| author | Luiz, José Lucas P. Miranda, Vinícius C. C. |
| author_facet | Luiz, José Lucas P. Miranda, Vinícius C. C. |
| contents | In this paper we study the norm-attainment of positive operators between Banach lattices. By considering an absolute version of James boundaries, we prove that: If $E$ is a reflexive Banach lattice whose order is given by a basis and $F$ is a Dedekind complete Banach lattice, then every positive operator from $E$ to $F$ is compact if and only if every positive operator from $E$ to $F$ attains its norm. An analogue result considering that $E$ is reflexive and the order in $F$ is continuous and given by a basis was proven. We applied our result to study a positive version of the weak maximizing property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On norm-attaining positive operators between Banach lattices Luiz, José Lucas P. Miranda, Vinícius C. C. Functional Analysis In this paper we study the norm-attainment of positive operators between Banach lattices. By considering an absolute version of James boundaries, we prove that: If $E$ is a reflexive Banach lattice whose order is given by a basis and $F$ is a Dedekind complete Banach lattice, then every positive operator from $E$ to $F$ is compact if and only if every positive operator from $E$ to $F$ attains its norm. An analogue result considering that $E$ is reflexive and the order in $F$ is continuous and given by a basis was proven. We applied our result to study a positive version of the weak maximizing property. |
| title | On norm-attaining positive operators between Banach lattices |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2409.14625 |