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

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URI: http://hdl.handle.net/10498/23592

DOI: 10.3390/math8071066

ISSN: 2227-7390

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Author/s
Moreno Pulido, SoledadAuthority UCA; Barbieri, Giuseppina; León Saavedra, FernandoAuthority UCA; Pérez Fernández, Francisco JavierAuthority UCA; Sala Pérez, AntonioAuthority UCA
Date
2020-07
Department
Matemáticas
Source
Mathematics 2020, 8(7), 1066
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.
Subjects
lacunary statistical summability; strong lacunary summability; weak unconditionally Cauchy series
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Atribución 4.0 Internacional
This work is under a Creative Commons License Atribución 4.0 Internacional