2026, Vol. 7, Issue 1, Part A
Matrix domains of Maddox-type Paranormed sequence spaces induced by Norlund matrices from combinatorial sequences
Author(s): Anil Singh and Mudasir Ahmad Lone
Abstract: We study matrix domains of paranormed sequence spaces obtained by applying lower triangular (triangle) matrices to Maddox-type variable-exponent spaces. A flexible family of such triangles is produced by N¨orlund matrices generated from admissible weight sequences, including Fibonacci, Pell, Motzkin, and Catalan numbers. For a base paranormed FK-space X ⊆ ω and a triangle A, the associated matrix domain XA = {x∈ω: Ax∈X} is equipped with the transported paranorm qA(x) = qX(Ax). We prove that completeness and the FK-structure pass from X to XA, that XA is (isometrically) isomorphic to X via the map x→ Ax, and that Schauder bases are preserved under passage to matrix domains. Finally, we describe the K¨othe-Toeplitz α-, β-, and γ-duals of XA in terms of the corresponding duals of X and the inverse triangle A−1, and we specialize the general results to N¨orlund matrices arising from classical integer sequences.
DOI: https://doi.org/10.22271/math.2026.v7.i1a.279
Pages: 06-12 | Views: 108 | Downloads: 38
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How to cite this article:
Anil Singh and Mudasir Ahmad Lone. Matrix domains of Maddox-type Paranormed sequence spaces induced by Norlund matrices from combinatorial sequences. Journal of Mathematical Problems, Equations and Statistics. 2026; 7(1): 06-12. DOI: 10.22271/math.2026.v7.i1a.279
