This theorem reveals properties of matrix transformations in sequence spaces, suggesting implications for convergence analysis.
We prove a Steinhaus-type theorem for four-dimensional matrix transformations of double sequences, establishing that (L_1, L_1, P ) ∩ (L_s, L_1) = ∅ , 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.
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Hamid et al. (2025) studied this question.
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