Let , r ≥ 0, be a triangle and q = ( q j ) be a bounded sequence of strictly positive numbers. In this paper, we study the algebraic and topological properties of the paranormed sequence space , generated by the triangle over Maddox′s space ℓ ( q ). We identify the Schauder basis as well as the α ‐, β ‐, and γ ‐duals of the space . One section is devoted to characterizing matrix classes , where is any of the spaces ℓ ∞ , c , and c 0 , and also presents the characterization of some other matrix classes related to the space as corollaries derived from a main result. The final section explores the geometric properties of the space .
Gan et al. (Thu,) studied this question.