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arXiv · 2402.06369

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·Antonio Sala-Pérez
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Abstract

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

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Soledad Moreno-Pulido, Giuseppina Barbieri, Fernando León-Saavedra, Francisco Javier Pérez-Fernández, Antonio Sala-Pérez. 2024-02-09. Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities. https://doi.org/10.3390/math8071066

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