Disjointly non-singular operators on Banach lattices

Manuel González; Antonio Martí nez-Abejón; Antonio Martinón

paper

Disjointly non-singular operators on Banach lattices

arXiv:2012.10683

Abstract

An operator $T$ from a Banach lattice $E$ into a Banach space is disjointly non-singular ( $D N$ - $S$ , for short) if no restriction of $T$ to a subspace generated by a disjoint sequence is strictly singular. We obtain several results for $D N$ - $S$ operators, including a perturbative characterization. For $E = L_{p}$ ( $1 < p < \infty$ ) we improve the results, and we show that the $D N$ - $S$ 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.