Abstract
In this paper we give several new results concerning domination problem in the setting of positive operators between Banach lattices. Mainly, it is proved that every positive operator \(R\) on a Banach lattice \(E\) dominated by an almost weakly compact operator \(T\) satisfies that the \(R^2\) is almost weakly compact. Domination by strictly singular operators is also considered. Moreover, we present some interesting connections between strictly singular, disjointly strictly singular and almost weakly compact operators.
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