Operators whose adjoints and second adjoints are almost Dunford-Pettis
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913523938885632 |
|---|---|
| author | Botelho, Geraldo Garcia, Luis Alberto |
| author_facet | Botelho, Geraldo Garcia, Luis Alberto |
| contents | First we characterize the Banach lattices E whose biduals have the positive Schur property by means of second adjoints of operators on E being almost Dunford-Pettis. Next we extend some known results concerning conditions on the Banach lattices E and F under which the adjoint T* and the second adjoint T** of any positive almost Dunford-Pettis operator T from E to F are almost Dunford-Pettis. Finally, we prove when T* and T** are almost Dunford-Pettis for any (non necessarily almost Dunford-Pettis) T that is either bounded, regular, order bounded or weakly compact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_11105 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Operators whose adjoints and second adjoints are almost Dunford-Pettis Botelho, Geraldo Garcia, Luis Alberto Functional Analysis 46B42, 47B07, 47B65 First we characterize the Banach lattices E whose biduals have the positive Schur property by means of second adjoints of operators on E being almost Dunford-Pettis. Next we extend some known results concerning conditions on the Banach lattices E and F under which the adjoint T* and the second adjoint T** of any positive almost Dunford-Pettis operator T from E to F are almost Dunford-Pettis. Finally, we prove when T* and T** are almost Dunford-Pettis for any (non necessarily almost Dunford-Pettis) T that is either bounded, regular, order bounded or weakly compact. |
| title | Operators whose adjoints and second adjoints are almost Dunford-Pettis |
| topic | Functional Analysis 46B42, 47B07, 47B65 |
| url | https://arxiv.org/abs/2207.11105 |