This is an announcement for the paper "Banach lattice versions of strict singularity" by Julio Flores, Jordi Lopez-Abad, and Pedro Tradacete.
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.
Archive classification: math.FA
Mathematics Subject Classification: 46B42, 47B60
Submitted from: ptradace@math.uc3m.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.4752
or