This research identifies matrix transformations and compact operators within generalized Motzkin sequence spaces, suggesting new topological insights.
In this article, we have constructed generalized q -difference Motzkin sequence spaces M0q(Δqm) , Mcq(Δqm) , Mpq(Δqm) and M∞q(Δqm) by composing q -Motzkin matrix with generalized q -difference matrix in the spaces c0,c,lp,l∞ , respectively and explore their topological properties. We determine the bases for Mcq(Δqm) and M0q(Δqm) and compute α -, β - and γ -duals of the newly defined spaces. Further, we characterize some class of matrix mappings from the spaces M0q(Δqm) and Mcq(Δqm) to the spaces c,c0,cs,cs0,l∞,l1,bs . Lastly, compact operators are characterized on the spaces M0q(Δqm) using Hausdorff measure of noncompactness.
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Quan et al. (2025) studied this question.
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