Geodesic
L-weakly and M-weakly demicompact operators on Banach lattices
Filomat, Tome 36 (2022) no. 13, p. 4319

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DOI

In this paper, we introduce and investigate new concepts of L-weakly and M-weakly demicompact operators. Let E be a Banach lattice. An operator T : E −→ E is called L-weakly demicompact, if for every norm bounded sequence (x n) in B E such that {x n − Tx n , n ∈ N} is an L-weakly compact subset of E, we have {x n , n ∈ N} is an L-weakly compact subset of E. Additionally, an operator T : E −→ E is called M-weakly demicompact if for every norm bounded disjoint sequence (x n) in E such that ∥x n − Tx n ∥ → 0, we have ∥x n ∥ → 0. L-weakly (resp. M-weakly) demicompact operators generalize known classes of operators which are L-weakly (resp. M-weakly) compact operators. We also elaborate some properties of these classes of operators.
DOI : 10.2298/FIL2213319B
Classification : 46B07, 46B42, 47B50
Keywords: Banach lattice, Order continuous norm, L-weakly compact operator, M-weakly compact operator, Demicompact operator, Order weakly demicompact operator, mandatory 
Hedi Benkhaled; Mohamed Hajji; Aref Jeribi. L-weakly and M-weakly demicompact operators on Banach lattices. Filomat, Tome 36 (2022) no. 13, p. 4319 . doi: 10.2298/FIL2213319B
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     title = {L-weakly and {M-weakly} demicompact operators on {Banach} lattices},
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     pages = {4319 },
     year = {2022},
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     doi = {10.2298/FIL2213319B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2213319B/}
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