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

Geraldo Botelho; José Lucas P. Luiz

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

Authors

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

Keywords:

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.

Issue

Vol. 46 No. 2 (2021)

Section

Articles

Published

2021-08-02

How to Cite

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. Retrieved from https://afm.journal.fi/article/view/110565

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