Infinite matrices with ``few'' non-zero entries and without non-trivial invariant subspaces (Q1011421)

This paper investigates a family of infinite matrices acting on \(\ell^1\) and derives a sufficient condition for a matrix in the family to have no nontrivial closed invariant subspaces. As a result, the author presents another operator without closed nontrivial invariant subspaces. The example matrix shown in the paper has all non-negative entries but one, which brings us closer to the negative answer to the invariant subspace problem for positive operators.