On linear sections of orthogonally additive operators
Our first result asserts that, for linear regular operators acting from a Riesz space with the principal projection property to a Banach lattice with an order continuous norm, the $C$-compactness is equivalent to the $AM$-compactness. Next we prove that, under mild assumptions, every linear section...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2022-10-01
|
| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/332 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Our first result asserts that, for linear regular operators acting from a Riesz space with the principal projection property to a Banach lattice with an order continuous norm, the $C$-compactness is equivalent to the $AM$-compactness. Next we prove that, under mild assumptions, every linear section of a $C$-compact orthogonally additive operator is $AM$-compact, and every linear section of a narrow orthogonally additive operator is narrow. |
|---|---|
| ISSN: | 1027-4634 2411-0620 |