Vector-valued spaces of multiplier statistically convergent series and uniform convergence

Abstract

In this paper, we introduce the spaces of vector-valued sequences containing multiplier (weakly) statistically convergent series. The completeness of such spaces is studied as well as some relations between unconditionally convergent and weakly unconditionally Cauchy series of these spaces. We also obtain generalizations of some results regarding uniform convergence of unconditionally convergent series through the concept of statistical convergence. Finally, we provide a version of the Orlicz-Pettis theorem for $\lambda$ -multiplier convergent operator series by means of the statistical convergence.