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 $$R$$ R on a Banach lattice $$E$$ E dominated by an almost weakly compact operator $$T$$ T satisfies that the $$R^2$$ 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.
Positivity – Springer Journals
Published: Feb 4, 2015
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