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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 throughN θandS θis obtained. We also relate the summability spaces associated with these summabilities with the strong p-Cesàro convergence summability space.

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