Geodesic
On the Schur, positive Schur and weak Dunford–Pettis properties in Fréchet lattices
Geraldo Botelho1 ; José Lucas P. Luiz2
1Universidade Federal de Uberlândia, Faculdade de Matemática
2IMECC-UNICAMP, Departamento de Matemática
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 633-642
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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.  
Keywords: Banach lattices, Fréchet lattices, Schur and positive Schur properties, dual positive Schur property, weak Dunford-Pettis property

Geraldo Botelho  1   ; José Lucas P. Luiz  2

1 Universidade Federal de Uberlândia, Faculdade de Matemática
2 IMECC-UNICAMP, Departamento de Matemática 
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Geraldo Botelho; José Lucas P. Luiz. On the Schur, positive Schur and weak Dunford–Pettis properties in Fréchet lattices. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 633-642. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a2/