Geodesic
A Steinhaus-Type Theorem for Multi-Dimensional Matrix Transformations in $(\mathcal L_1,\mathcal L_1)$
Publications de l'Institut Mathématique, _N_S_118 (2025) no. 132, p. 67

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DOI

We prove a Steinhaus-type theorem for four-dimensional matrix transformations of double sequences, establishing that $(\mathcal L_1,\mathcal L_1,P)\cap(\mathcal L_s,\mathcal L_1)=\emptyset$, $s>1$. This extends Fridy's classical result for single sequences. Our results hold for sequences of bounded variation, bounded, Pringsheim convergent, bounded Pringsheim convergent, and regularly convergent sequence spaces. We show this theorem fails in non-archimedean fields through a counterexample.
DOI : 10.2298/PIM2532067H
Classification : 40B05, 40C05
Keywords: double sequences, four-dimensional matrices, Steinhaus-type theorem 
Sami M. Hamid; Richard F. Patterson. A Steinhaus-Type Theorem for Multi-Dimensional Matrix Transformations in $(\mathcal L_1,\mathcal L_1)$. Publications de l'Institut Mathématique, _N_S_118 (2025) no. 132, p. 67 . doi: 10.2298/PIM2532067H
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     journal = {Publications de l'Institut Math\'ematique},
     pages = {67 },
     year = {2025},
     volume = {_N_S_118},
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     doi = {10.2298/PIM2532067H},
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