Banach lattice versions of strict singularity
Functional Analysis
2014-10-20 v1
Abstract
We explore the relation between lattice versions of strict singularity for operators from a Banach lattice to a Banach space. In particular, we study when the class of disjointly strictly singular operators, those not invertible on the span of any disjoint sequence, coincides with that of lattice strictly singular operators, i.e. those not invertible on any (infinite dimensional) sublattice. New results are given which help to clarify the existing relation between these two classes.
Cite
@article{arxiv.1410.4752,
title = {Banach lattice versions of strict singularity},
author = {Julio Flores and Jordi López-Abad and Pedro Tradacete},
journal= {arXiv preprint arXiv:1410.4752},
year = {2014}
}