On the Schur, positive Schur and weak Dunford–Pettis properties in Fréchet lattices

Författare

  • Geraldo Botelho Universidade Federal de Uberlândia, Faculdade de Matemática
  • José Lucas P. Luiz IMECC-UNICAMP, Departamento de Matemática

Nyckelord:

Banach lattices, Fréchet lattices, Schur and positive Schur properties, dual positive Schur property, weak Dunford-Pettis property

Abstract

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.

 

Sektion
Articles

Publicerad

2021-08-02

Referera så här

Botelho, G., & Luiz, J. L. P. (2021). On the Schur, positive Schur and weak Dunford–Pettis properties in Fréchet lattices. Annales Fennici Mathematici, 46(2), 633–642. Hämtad från https://afm.journal.fi/article/view/110565