1 results
Some results on various types of compactness of weak* Dunford–Pettis operators on Banach lattices
- Part of
-
- Journal:
- Canadian Mathematical Bulletin / Volume 67 / Issue 2 / June 2024
- Published online by Cambridge University Press:
- 23 October 2023, pp. 403-414
- Print publication:
- June 2024
-
- Article
-
- You have access
- HTML
- Export citation
-
We study the relationship between weak* Dunford–Pettis and weakly (resp. M-weakly, order weakly, almost M-weakly, and almost L-weakly) operators on Banach lattices. The following is one of the major results dealing with this matter: If E and F are Banach lattices such that F is Dedekind
$\sigma $-complete, then each positive weak* Dunford–Pettis operator 
$T:E\rightarrow F$ is weakly compact if and only if one of the following assertions is valid: (a) the norms of 
$E^{\prime }$ and F are order continuous; (b) E is reflexive; and (c) F is reflexive.
