Journal
FILOMAT
Volume 36, Issue 13, Pages 4319-4329Publisher
UNIV NIS, FAC SCI MATH
DOI: 10.2298/FIL2213319B
Keywords
Banach lattice; Order continuous norm; L-weakly compact operator; M-weakly compact operator; Demicompact operator; Order weakly demicompact operator; mandatory
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In this paper, new concepts of L-weakly and M-weakly demicompact operators are introduced and investigated. The definitions of these operators are provided, and some properties of these two classes of operators are discussed.
In this paper, we introduce and investigate new concepts of L-weakly and M-weakly demicom-pact operators. Let E be a Banach lattice. An operator T : E --> E is called L-weakly demicompact, if for every norm bounded sequence (xn) in BE such that {xn - Txn, n is an element of N} is an L-weakly compact subset of E, we have {xn, n is an element of 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 (xn) in E such that parallel to xn - Txn parallel to -> 0, we have parallel to xn parallel to -> 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.
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