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Open AccessArticle

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

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Department of Mathematics, College of Engineering, University of Cadiz, 11510 Puerto Real, Spain
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Department of Mathematics, University of Salerno, via Giovanni Paolo II, 84084 Fisciano (SA), Italy
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Department of Mathematics, Faculty of Social Sciences and Communication, University of Cádiz, 11403 Jerez de la Frontera, Spain
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Department of Mathematics, Faculty of Sciences, University of Cádiz, 11510 Puerto Real, Spain
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(7), 1066; https://doi.org/10.3390/math8071066
Received: 11 June 2020 / Revised: 22 June 2020 / Accepted: 23 June 2020 / Published: 2 July 2020
(This article belongs to the Special Issue Functional Analysis, Topology and Quantum Mechanics)
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. View Full-Text
Keywords: lacunary statistical summability; strong lacunary summability; weak unconditionally Cauchy series lacunary statistical summability; strong lacunary summability; weak unconditionally Cauchy series
MDPI and ACS Style

Moreno-Pulido, S.; Barbieri, G.; León-Saavedra, F.; Pérez-Fernández, F.J.; Sala-Pérez, A. Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities. Mathematics 2020, 8, 1066.

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