On an open question concerning the domination problem in the class of almost BS-compact operators

The goal of this note is to give a positive answer to the problem 4.11 in [Almost BS-compact operators and domination problem, Mediterr. J. Math. 18, 258 (2021)]. More precisely, we proved that if a positive operator R on a Banach lattice E is dominated by an almost BS-compact operator \(T: E \rightarrow E\), then \(R^2\) is almost BS-compact.