On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal. (14th April 2022)

• Record Type: Journal Article
• Authors: Yaying, Taja; Hazarika, Bipan; Mohamed, O. M. Kalthum S. K.; Bakery, Awad A.
• Other Names: nar Muhammed Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-04-14
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/8269000
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In the present study, we have constructed new Banach sequence spaces ℓ p L, c 0 L, c L, and ℓ ∞ L, where L = l v, k is a regular matrix defined by l v, k = l k / l v + 2 − v + 2, 0 ≤ k ≤ v, 0, k > v, for all v, k = 0, 1, 2, ⋯, where l = l k is a sequence of Leonardo numbers. We study their topological and inclusion relations and construct Schauder bases of the sequence spaces ℓ p L, c 0 L, and c L . Besides, α -, β - and γ -duals of the aforementioned spaces are computed. We state and prove results of the characterization of the matrix classes between the sequence spaces ℓ p L, c 0 L, c L, and ℓ ∞ L to any one of the spaces ℓ 1, c 0, c, and ℓ ∞ . Finally, under a definite functional ρ and a weighted sequence of positive reals r, we introduce new sequence spaces c 0 L, r ρ and ℓ p L, r ρ . We present some geometric and topological properties of these spaces, as well as the eigenvalue distribution of ideal mappings generated by these spaces and s -numbers.