Domination by positive Banach–Saks operators
Volume 173 / 2006
Studia Mathematica 173 (2006), 185-192 MSC: Primary 47B65; Secondary 46B20. DOI: 10.4064/sm173-2-5
Given a positive Banach–Saks operator $T$ between two Banach lattices $E$ and $F$, we give sufficient conditions on $E$ and $F$ in order to ensure that every positive operator dominated by $T$ is Banach–Saks. A counterexample is also given when these conditions are dropped. Moreover, we deduce a characterization of the Banach–Saks property in Banach lattices in terms of disjointness.