Title of article
Almost order-weakly compact operators on Banach lattices
Author/Authors
Pazira ، Mohammad Department of Mathematics and Applications - Faculty of Sciences - University of Mohaghegh Ardabili , Matin ، Mina Department of Mathematics and Applications - Faculty of Sciences - University of Mohaghegh Ardabili , Haghnejad Azar ، Kazem Department of Mathematics and Applications - Faculty of Sciences - University of Mohaghegh Ardabili , Abadi ، Ali Department of Mathematics and Applications - Faculty of Sciences - University of Mohaghegh Ardabili
From page
353
To page
360
Abstract
A continuous operator T between two Banach lattices E and F is called almost order-weakly compact, whenever for each almost order bounded subset A of E, T(A) is a relatively weakly compact subset of F. We show that the positive operator T from E into a Dedekind complete Banach lattice F is almost order-weakly compact iff T(xn) ∥.∥ −−→ 0 in F for each disjoint almost order bounded sequence {xn} in E. In this manuscript, we study some properties of this class of operators and its relationships with the others known classes of operators.
Keywords
almost order bounded , weakly compact , order weakly compact , almost order , weakly compact
Journal title
International Journal of Nonlinear Analysis and Applications
Journal title
International Journal of Nonlinear Analysis and Applications
Record number
2773615
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