Matrix characterization of \(A\)-statistical convergence of double sequences (Q397012)

Some results of \textit{M. K. Khan} and \textit{C. Orhan} [J. Math. Anal. Appl. 335, No. 1, 406--417 (2007; Zbl 1123.40003)] on regular matrices and statistical summability are extended to double sequences. For four-dimensional matrices, the authors prove a bounded consistency theorem and characterize the multiplier spaces of summability domains. It turns out that for a nonnegative RH-regular matrix \(A=(a_{jk}^{mn})\), this multiplier space coincides with the space of all \(A\)-statistically convergent double sequences. Moreover, the authors show that for \(A\)-uniformly integrable double sequences, the \(A\)-statistical convergence is equivalent to the \(B\)-summability, where \(B=(b_{jk}^{mn})\) is a (suitable chosen) nonnegative RH-regular matrix.