On the Schur, positive Schur and weak Dunford-Pettis properties in Fr\'echet lattices

Autor:	Botelho, Geraldo, Luiz, José Lucas P.
Rok vydání:	2019
Předmět:	Mathematics - Functional Analysis 46A40 46B42 46A04
Druh dokumentu:	Working Paper
Popis:	We prove some general results on sequential convergence in Fr\'echet 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. Comment: 11 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1909.09514 Zobrazit plný text záznamu View this record from Arxiv