Orlicz-Pettis Theorem through Summability Methods

被引：6

作者：

Leon-Saavedra, Fernando ^{[1
]}

Romero de la Rosa, Maria del Pilar ^{[2
]}

Sala, Antonio ^{[3
]}

机构：

[1] Univ Cadiz, Dept Math, Fac Ciencias Sociales & Comunicac, Cadiz 11405, Spain

[2] Univ Cadiz, Dept Math, Cadiz 11510, Spain

[3] Univ Cadiz, Dept Matemat, Escuela Super Ingn, Cadiz 11510, Spain

来源：

MATHEMATICS | 2019年 / 7卷 / 10期

关键词：

summability method; ideal convergence; weakly unconditional Cauchy series; Orlicz-Pettis theorem; CAUCHY; SERIES;

D O I：

10.3390/math7100895

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper unifies several versions of the Orlicz-Pettis theorem that incorporate summability methods. We show that a series is unconditionally convergent if and only if the series is weakly subseries convergent with respect to a regular linear summability method. This includes results using matrix summability, statistical convergence with respect to an ideal, and other variations of summability methods.

引用

页数：5

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