Banach space

Pure mathematics

Discrete mathematics

Essential singularity

Approximation property

Singularity

Acoustics

Lattice (music)

Physics

Mathematics

Mathematical analysis

Invertible matrix

Disjoint sets

Journal of Functional Analysis

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.

Banach lattice versions of strict singularity