Almost order-weakly compact operators on Banach lattices

2022/01/06 by Matin, Mina, Mina Matin, Kazem Haghnejad Azar +3
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.2201.02219

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. In Theorem 4, we show that the positive operator T from E into Dedekind complete F is almost order-weakly compact if and only if T(x_n) \xrightarrow‖.‖0 in F for each disjoint almost order bounded sequence \x_n\ in E. In this manuscript, we study some properties of this class of operators and its relationships with others known operators.

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