Multiplier Sequence Spaces Defined by Statistical Summability and Orlicz-Pettis Theorem

In this paper, we introduce some new multiplier spaces related to a series ∑ixi in a normed space X through f–statistical summability and give some characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in X and X*, respectively. We also obtain a new version of the Orlicz-Pettis theorem within the frame of the f–statistical convergence.