On the Schur, positive Schur and weak Dunford–Pettis properties in Fréchet lattices - Botelho, Geraldo; Luiz, José Lucas P. (Annales Fennici Mathematici, 2021)
We prove some general results on sequential convergence in Fréchet lattices that yield, as particular instances, the following results regarding a closed ideal \(I\) of a Banach lattice \(E\): (i) If two of the lattices \(E\), \(I\) and \(E/I\) have the positive Schur property (the Schur property, respectively) then the third lattice has the positive Schur property (the Schur property, respectively) as well; (ii) If \(I\) and \(E/I\) have the dual positive Schur property, then \(E\) also has this property; (iii) If \(I\) has the weak Dunford-Pettis property and \(E/I\) has the positive Schur property, then \(E\) has the weak Dunford-Pettis property. Examples and applications are provided.