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On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal
In the present study, we have constructed new Banach sequence spaces ℓpL,c0L,cL, and ℓ∞L, where L=lv,k is a regular matrix defined by lv,k=lk/lv+2−v+2, 0≤k≤v,0, k>v, for all v,k=0,1,2,⋯, where l=lk is a sequence of Leonardo numbers. We study their topological and inclusion relations and construct...
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Published in: | Journal of function spaces 2022, Vol.2022, p.1-21 |
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description | In the present study, we have constructed new Banach sequence spaces ℓpL,c0L,cL, and ℓ∞L, where L=lv,k is a regular matrix defined by lv,k=lk/lv+2−v+2, 0≤k≤v,0, k>v, for all v,k=0,1,2,⋯, where l=lk is a sequence of Leonardo numbers. We study their topological and inclusion relations and construct Schauder bases of the sequence spaces ℓpL,c0L, and cL. 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 ℓpL,c0L,cL, and ℓ∞L to any one of the spaces ℓ1,c0,c, and ℓ∞. Finally, under a definite functional ρ and a weighted sequence of positive reals r, we introduce new sequence spaces c0L,rρ and ℓpL,rρ. 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. |
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M. Kalthum S. K. ; Bakery, Awad A.</creator><contributor>nar, Muhammed ; Muhammed nar</contributor><creatorcontrib>Yaying, Taja ; Hazarika, Bipan ; Mohamed, O. M. Kalthum S. K. ; Bakery, Awad A. ; nar, Muhammed ; Muhammed nar</creatorcontrib><description>In the present study, we have constructed new Banach sequence spaces ℓpL,c0L,cL, and ℓ∞L, where L=lv,k is a regular matrix defined by lv,k=lk/lv+2−v+2, 0≤k≤v,0, k>v, for all v,k=0,1,2,⋯, where l=lk is a sequence of Leonardo numbers. We study their topological and inclusion relations and construct Schauder bases of the sequence spaces ℓpL,c0L, and cL. 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 ℓpL,c0L,cL, and ℓ∞L to any one of the spaces ℓ1,c0,c, and ℓ∞. Finally, under a definite functional ρ and a weighted sequence of positive reals r, we introduce new sequence spaces c0L,rρ and ℓpL,rρ. 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.</description><identifier>ISSN: 2314-8896</identifier><identifier>EISSN: 2314-8888</identifier><identifier>DOI: 10.1155/2022/8269000</identifier><language>eng</language><publisher>New York: Hindawi</publisher><subject>Eigenvalues ; Numbers ; Topology</subject><ispartof>Journal of function spaces, 2022, Vol.2022, p.1-21</ispartof><rights>Copyright © 2022 Taja Yaying et al.</rights><rights>Copyright © 2022 Taja Yaying et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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title | On New Banach Sequence Spaces Involving Leonardo Numbers and the Associated Mapping Ideal |
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