标题： Gelfand-Phillips型性质在巴拿赫格中 显示英文标题

标题： Gelfand-Phillips-type properties in Banach lattices

摘要： 我们研究巴拿赫格上$p$限制和几乎$p$限制的集合及其与相对$p$紧和相对紧集合之间的联系。 我们研究了序$p$的弱和强 Gelfand-Phillips 性质，以及 Delgado 和 Piñeiro 引入的$p$-GP 性质，并提供了这些性质可能一致的条件。 此外，我们证明了巴拿赫格 $E$ 是一个 KB-空间当且仅当 $E$ 中每一个几乎 $p$-有限集都是相对弱紧的当且仅当每个取值于 $E$ 的弱紧算子的共轭都是不相交 $p$-求和的。 显示英文摘要

摘要： We study $p$-limited and almost $p$-limited sets in Banach lattices and their connections with relatively $p$-compact and relatively compact sets. We investigate the weak and the strong Gelfand-Phillips property of order $p$, as well as the $p$-GP property introduced by Delgado and Pi\~neiro, providing conditions under which these properties may coincide. Additionally, we prove that a Banach lattice $E$ is a KB-space if and only if every almost $p$-limited set in $E$ is relatively weakly compact if and only if every the adjoint of a weakly compact taking values on $E$ is disjoint $p$-summing.