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Schur Lemma and Uniform Convergence of Series through Convergence Methods

Author

Listed:
  • Fernando León-Saavedra

    (Regional Mathematical Center of Southern Federal University, Rostov-on-Don, Russia & Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, 11405 Jerez de la Frontera (Cádiz), Spain)

  • María del Pilar Romero de la Rosa

    (Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, 11405 Jerez de la Frontera (Cádiz), Spain)

  • Antonio Sala

    (Department of Mathematics, University of Cádiz, Avenida de la Universidad s/n, 11510 Puerto Real (Cádiz), Spain)

Abstract

In this note, we prove a Schur-type lemma for bounded multiplier series. This result allows us to obtain a unified vision of several previous results, focusing on the underlying structure and the properties that a summability method must satisfy in order to establish a result of Schur’s lemma type.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1744-:d:426230
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    References listed on IDEAS

    as
    1. 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.
    2. Fernando León-Saavedra & Francisco Javier Pérez-Fernández & María del Pilar Romero de la Rosa & Antonio Sala, 2019. "Ideal Convergence and Completeness of a Normed Space," Mathematics, MDPI, vol. 7(10), pages 1-11, September.
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