论文标题
Banach Lattices中的弱压缩性
Weak precompactness in Banach lattices
论文作者
论文摘要
我们表明，当$ e $中的每个订单间隔都是弱的，或者，仅当且仅当每个弱点弱紧凑的集合都是弱的预发时，且仅当每个订单间隔都是弱的，或者等效地，当时的每个订单间隔都是薄弱的。获得了弱预校准正算子的支配性能的一些结果。除其他外，我们表明，对于一对Banach Lattices $ e $和$ f $，带有$ e $ $ $σ$ -Dedekind完整，每个正运算符从$ e $到$ e $ to $ f $由虚弱的预发操作员统治，并且仅当$ e^{\ prime} $ contere contres contres contres contres contres contere contere contere nister contercoct或nive $ fiff $ fiff y Intercoct均为$ FIST $ FIST $ FISTARTIS $ FISTART $ FISTACT。
We show that the solid hull of every weakly precompact set of a Banach lattice $E$ is weakly precompact if and only if every order interval in $E$ is weakly precompact, or equivalently, if and only if every disjoint weakly compact set is weakly precompact. Some results on the domination property for weakly precompact positive operators are obtained. Among other things, we show that, for a pair of Banach lattices $E$ and $F$ with $E$ $σ$-Dedekind complete, every positive operator from $E$ to $F$ dominated by a weakly precompact operator is weakly precompact if and only if either the norm of $E^{\prime}$ is order continuous or else every order interval in $F$ is weakly precompact.
