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arXiv · 2201.02219

Almost order-weakly compact operators on Banach lattices

Mina Matin·Kazem Haghnejad Azar·Ali Ebadi
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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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Mina Matin, Kazem Haghnejad Azar, Ali Ebadi. 2022-01-06. Almost order-weakly compact operators on Banach lattices. https://arxiv.org/abs/2201.02219

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