## 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

Zbl 0675.40004
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