论文标题
在Banach Lattices上几乎有序紧凑的操作员
Almost order-weakly compact operators on Banach lattices
论文作者
论文摘要
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 $F$.在定理4中，我们表明，当且仅当$ t（x_n）\ xrightArrow {\ xrightArrow {\ |。|。|。|。|。|。|。|。|。|。在此手稿中，我们研究了此类运营商的某些特性及其与其他知名运营商的关系。
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.
