Matrix characterization of A-statistical convergence of double sequences

Abstract

We characterize the multiplier space of summability fields of four dimensional RH-regular matrices and show that the space of multipliers of a nonnegative RH-regular matrix over an algebra \(\mathcal{U} \) is the space of A-statistically convergent double sequences. For this purpose we prove a variant of the Brudno–Mazur–Orlicz bounded consistency theorem for a class of four dimensional matrices. Finally we give a matrix characterization of A-statistical convergence over the space of the Pringsheim A-uniformly integrable double sequences.