Matrix characterization of A-statistical convergence

The main objective of the paper is to characterize multipliers of summability fields of regular methods, while relaxing the usual boundedness condition. For this purpose we use the sequence spaces of A-bounded sequences and A-uniformly integrable sequences. Among the main results, it is shown that the space of multipliers is closely related to the space of A-statistically convergent sequences and that A-statistical convergence over ℓ∞ is equivalent to a regular matrix method. This observation eliminates the need for separate proofs of several A-statistical convergence results.