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

Abstract

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.

Keywords

• lacunary statistical summability
• strong lacunary summability
• weak unconditionally Cauchy series