L-weakly and M-weakly Demicompact Operators On Banach Lattices

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.

Automated summary

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.