Some results on almost L-weakly and almost M-weakly compact operators

Nouira, Redouane; Lhaimer, Driss; Elbour, Aziz

doi:10.1007/s11117-022-00911-3

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Almost M-weak and Almost L-weak Compactness Of Weak* Dunford...1

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2024

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Cited by 4 publications

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“…The notion of almost M-weakly (and almost L-weakly) compact operators was introduced in [8] and studied in [14, 19]. An operator T from a Banach lattice E into a Banach space Y is called almost M-weakly compact if for every bounded and disjoint sequence in E , and every weakly convergent sequence of Y , we have .…”

Section: Almost M-weak and Almost L-weak Compactness Of Weak* Dunford...mentioning

confidence: 99%

Some results on various types of compactness of weak^* Dunford–Pettis operators on Banach lattices

Nouira,

Aqzzouz

2023

Can. Math. Bull.

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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.

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