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

Abstract

In this paper, we introduce some new multiplier spaces related to a series Sigma(i)x(i) 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.