论文标题
在Banach Lattices上脱节的非单明操作员
Disjointly non-singular operators on Banach lattices
论文作者
论文摘要
如果不限制$ t $的子空间，那是不连接序列生成的子空间，则来自Banach Lattice $ e $从Banach Lattice $ e $中的运营商$ t $是不一致的非差异（$ dn $ - $ s $）。我们为$ DN $ -S $运算符获得了几个结果，包括扰动表征。对于$ e = l_p $（$ 1 <p <\ infty $），我们改善了结果，我们表明$ dn $ - $ s $运算符在情况下具有不同的行为，$ p = 2 $和$ p \ neq 2 $。作为一个应用程序，我们证明了$ l_p $的强嵌入子空间在所有封闭子空间集中形成一个打开子集。
An operator $T$ from a Banach lattice $E$ into a Banach space is disjointly non-singular ($DN$-$S$, for short) if no restriction of $T$ to a subspace generated by a disjoint sequence is strictly singular. We obtain several results for $DN$-$S$ operators, including a perturbative characterization. For $E=L_p$ ($1< p<\infty$) we improve the results, and we show that the $DN$-$S$ operators have a different behavior in the cases $p=2$ and $p\neq 2$. As an application we prove that the strongly embedded subspaces of $L_p$ form an open subset in the set of all closed subspaces.
