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We explore the relation between lattice versions of strict singularity foroperators from a Banach lattice to a Banach space. In particular, we study whenthe class of disjointly strictly singular operators, those not invertible onthe span of any disjoint sequence, coincides with that of lattice strictlysingular operators, i.e. those not invertible on any (infinite dimensional)sublattice. New results are given which help to clarify the existing relationbetween these two classes.

Banach lattice versions of strict singularity