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Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities

Author

Listed:
  • Soledad Moreno-Pulido

    (Department of Mathematics, College of Engineering, University of Cadiz, 11510 Puerto Real, Spain)

  • Giuseppina Barbieri

    (Department of Mathematics, University of Salerno, via Giovanni Paolo II, 84084 Fisciano (SA), Italy)

  • Fernando León-Saavedra

    (Department of Mathematics, Faculty of Social Sciences and Communication, University of Cádiz, 11403 Jerez de la Frontera, Spain)

  • Francisco Javier Pérez-Fernández

    (Department of Mathematics, Faculty of Sciences, University of Cádiz, 11510 Puerto Real, Spain)

  • Antonio Sala-Pérez

    (Department of Mathematics, College of Engineering, University of Cadiz, 11510 Puerto Real, Spain)

Abstract

In this manuscript we characterize the completeness of a normed space through the strong lacunary ( N θ ) and lacunary statistical convergence ( S θ ) of series. A new characterization of weakly unconditionally Cauchy series through N θ and S θ is obtained. We also relate the summability spaces associated with these summabilities with the strong p -Cesàro convergence summability space.

Suggested Citation

  • Soledad Moreno-Pulido & Giuseppina Barbieri & Fernando León-Saavedra & Francisco Javier Pérez-Fernández & Antonio Sala-Pérez, 2020. "Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities," Mathematics, MDPI, vol. 8(7), pages 1-10, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1066-:d:379314
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