×

Almost regular matrices for double sequences. (English) Zbl 1050.40003

The concept of almost convergence for double sequences was introduced by F. Móricz and B. E. Rhoades [Math. Proc. Camb. Philos. Soc. 104, No. 2, 283–294 (1988; Zbl 0675.40004)]. Denote by \(f_2\) the space of all almost convergent double sequences and by \(c^\infty_2\) the space of all double sequences that are bounded and convergent. A four-dimensional matrix \(A=(a_{jk}^{mn})\) is called almost regular by the authors if for every \(x=(x_{jk})\in c_2^\infty\) the double sequence \(Ax\) belongs to \(f_2\) and \(f_2\)-\(\lim Ax=\lim x\) (\(=\text{Pringsheim's}\) limit of \(x\)). The authors give necessary and sufficient conditions for a four-dimensional matrix to be almost regular.

MSC:

40C05 Matrix methods for summability
40D05 General theorems on summability

Citations:

Zbl 0675.40004
PDF BibTeX XML Cite
Full Text: DOI