Characterizations of a Banach Space through the Strong Lacunary and the Lacunary Statistical Summabilities
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Author/sMoreno-Pulido, Soledad; Barbieri, Giuseppina; León-Saavedra, Fernando; Pérez-Fernández, Francisco Javier; Sala Pérez, Antonio
SourceMathematics 2020, 8(7), 1066
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.