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

Soledad Moreno-Pulido, Giuseppina Barbieri, Fernando León-Saavedra, Francisco Javier Pérez-Fernández and Antonio Sala-Pérez
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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

Mathematics, 2020, vol. 8, issue 7, 1-10

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.

Keywords: lacunary statistical summability; strong lacunary summability; weak unconditionally Cauchy series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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