Geodesic
Some results on various types of compactness of weak* Dunford–Pettis operators on Banach lattices
Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 403-414

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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.
DOI : 10.4153/S000843952300084X
Mots-clés : Dunford–Pettis, weak* Dunford–Pettis operator, weakly compact operator, M-weakly compact operator, almost M-weakly compact operator 
Nouira, Redouane; Aqzzouz, Belmesnaoui. Some results on various types of compactness of weak* Dunford–Pettis operators on Banach lattices. Canadian mathematical bulletin, Tome 67 (2024) no. 2, pp. 403-414. doi: 10.4153/S000843952300084X
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     title = {Some results on various types of compactness of weak* {Dunford{\textendash}Pettis} operators on {Banach} lattices},
     journal = {Canadian mathematical bulletin},
     pages = {403--414},
     year = {2024},
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