Paranormed Norlund Nᵗ- difference sequence spaces and their α-, β- and γ-duals
DOI:
https://doi.org/10.22199/issn.0717-6279-5289Keywords:
paranormed sequence space, Nᵗ-Difference sequence space, Norlund matrix, Schauder basis, α-, β- and γ-dualsAbstract
Kizmaz [4] defined some difference spaces viz., ℓ∞ (∆), c(∆) and c0(∆) and studied by Et and Colak [1] thoroughly. In this paper, Norlund Nt- difference sequence spaces Nt(c0, p, ∆), Nt(c, p, ∆) and Nt(ℓ∞, p, ∆) contain the sequences whose Nt∆-transforms in c0, c and ℓ∞ are defined and the paranormed linear structures are developed on these spaces. It has been shown that the spaces Nt(c0, p, ∆), Nt(c, p, ∆) & Nt(ℓ∞, p, ∆) are linearly isomorphic and are of non-absolute type. Further, it is verified that Nt(c, p, ∆), Nt(c0, p, ∆)and Nt(l∞, p, ∆) of non-absolute form are isomorphic to Nt(c0, p), Nt(c, p) and Nt(ℓ∞, p), respectively. Topological properties such as the completeness and the isomorphism are also discussed. Some inclusion relations among these spaces are also verified. Finally, the α-, β- and γ- dual of these spaces are determined and constructed the Schauder-basis of Nt(c0, p, ∆) and Nt(c, p, ∆).
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