Orlicz–Pettis Theorem through Summability Methods

Fernando León-Saavedra, María del Pilar Romero de la Rosa and Antonio Sala
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Fernando León-Saavedra: Department of Mathematics, University of Cádiz, Facultad Ciencias Sociales y de la Comunicación, 11405 Jerez de la Frontera, Cádiz, Spain
María del Pilar Romero de la Rosa: Department of Mathematics, University of Cádiz, CASEM, 11510 Puerto Real, Cadiz, Spain
Antonio Sala: Departamento de Matemáticas, University of Cádiz, Escuela Superior de Ingeniería, 11510 Puerto Real, Cadiz, Spain

Mathematics, 2019, vol. 7, issue 10, 1-5

Abstract: 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.

Keywords: summability method; ideal convergence; weakly unconditional Cauchy series; Orlicz–Pettis theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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