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Orlicz–Pettis Theorem through Summability Methods

Author

Listed:
  • 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)

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.

Suggested Citation

  • Fernando León-Saavedra & María del Pilar Romero de la Rosa & Antonio Sala, 2019. "Orlicz–Pettis Theorem through Summability Methods," Mathematics, MDPI, vol. 7(10), pages 1-5, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:895-:d:270492
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    Cited by:

    1. María del Pilar Romero de la Rosa, 2023. "On Modulated Lacunary Statistical Convergence of Double Sequences," Mathematics, MDPI, vol. 11(4), pages 1-10, February.
    2. Fernando León-Saavedra & María del Pilar Romero de la Rosa & Antonio Sala, 2020. "Schur Lemma and Uniform Convergence of Series through Convergence Methods," Mathematics, MDPI, vol. 8(10), pages 1-11, October.

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