Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞
We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1⩽p⩽∞, respectively, and prove that ℓpλ(B) and ℓp are linearly isomorphic for 0<p⩽∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we co...
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Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/349346 |
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| author | Feyzi Başar Ali Karaisa |
| author_facet | Feyzi Başar Ali Karaisa |
| author_sort | Feyzi Başar |
| collection | DOAJ |
| description | We introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1⩽p⩽∞, respectively, and prove that ℓpλ(B) and ℓp are linearly isomorphic for 0<p⩽∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we construct the basis for the space ℓpλ(B), where 1⩽p<∞. Furthermore, we determine the alpha-, beta- and gamma-duals of the space ℓpλ(B) for 1⩽p⩽∞. Finally, we investigate some geometric properties concerning Banach-Saks type p and give Gurarii's modulus of convexity for the normed space ℓpλ(B). |
| format | Article |
| id | doaj-art-5ed4ed9d590d4a46b830ef33ccd3258d |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-5ed4ed9d590d4a46b830ef33ccd3258d2025-02-03T01:22:14ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/349346349346Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞Feyzi Başar0Ali Karaisa1Department of Mathematics, Faculty of Arts and Sciences, Fatih University, Hadımköy Campus, Büyükçekmece, 34500 İstanbul, TurkeyDepartment of Mathematics & Computer Science, Faculty of Science, Necmettin Erbakan University, Meram Campus, Meram, 42090 Konya, TurkeyWe introduce the sequence space ℓpλ(B) of none absolute type which is a p-normed space and BK space in the cases 0<p<1 and 1⩽p⩽∞, respectively, and prove that ℓpλ(B) and ℓp are linearly isomorphic for 0<p⩽∞. Furthermore, we give some inclusion relations concerning the space ℓpλ(B) and we construct the basis for the space ℓpλ(B), where 1⩽p<∞. Furthermore, we determine the alpha-, beta- and gamma-duals of the space ℓpλ(B) for 1⩽p⩽∞. Finally, we investigate some geometric properties concerning Banach-Saks type p and give Gurarii's modulus of convexity for the normed space ℓpλ(B).http://dx.doi.org/10.1155/2013/349346 |
| spellingShingle | Feyzi Başar Ali Karaisa Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞ The Scientific World Journal |
| title | Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞ |
| title_full | Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞ |
| title_fullStr | Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞ |
| title_full_unstemmed | Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞ |
| title_short | Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces ℓp and ℓ∞ |
| title_sort | some new generalized difference spaces of nonabsolute type derived from the spaces lp and l∞ |
| url | http://dx.doi.org/10.1155/2013/349346 |
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