Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A
Let X be a nonempty set, A be a commutative Banach algebra, and 1≤p<∞. In this paper, we present a concise proof for the result concerning the BSE (Banach space extension) property of ℓpX,A. Specifically, we establish that ℓpX,A possesses the BSE property if and only if X is finite and A is BSE....
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2024/5893357 |
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| author | Shirin Tavkoli Rasoul Abazari Ali Jabbari |
| author_facet | Shirin Tavkoli Rasoul Abazari Ali Jabbari |
| author_sort | Shirin Tavkoli |
| collection | DOAJ |
| description | Let X be a nonempty set, A be a commutative Banach algebra, and 1≤p<∞. In this paper, we present a concise proof for the result concerning the BSE (Banach space extension) property of ℓpX,A. Specifically, we establish that ℓpX,A possesses the BSE property if and only if X is finite and A is BSE. Additionally, we investigate the BSE module property on Banach ℓpX,A-modules and demonstrate that a Banach space ℓpX,Y serves as a BSE Banach ℓpX,A-module if and only if X is finite and Y represents a BSE Banach A-module. |
| format | Article |
| id | doaj-art-c995334cc28d40d3bb7a6c8d3ae54a9d |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-c995334cc28d40d3bb7a6c8d3ae54a9d2025-02-03T05:54:35ZengWileyJournal of Function Spaces2314-88882024-01-01202410.1155/2024/5893357Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,AShirin Tavkoli0Rasoul Abazari1Ali Jabbari2Department of MathematicsDepartment of MathematicsFaculty of ScienceLet X be a nonempty set, A be a commutative Banach algebra, and 1≤p<∞. In this paper, we present a concise proof for the result concerning the BSE (Banach space extension) property of ℓpX,A. Specifically, we establish that ℓpX,A possesses the BSE property if and only if X is finite and A is BSE. Additionally, we investigate the BSE module property on Banach ℓpX,A-modules and demonstrate that a Banach space ℓpX,Y serves as a BSE Banach ℓpX,A-module if and only if X is finite and Y represents a BSE Banach A-module.http://dx.doi.org/10.1155/2024/5893357 |
| spellingShingle | Shirin Tavkoli Rasoul Abazari Ali Jabbari Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A Journal of Function Spaces |
| title | Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A |
| title_full | Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A |
| title_fullStr | Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A |
| title_full_unstemmed | Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A |
| title_short | Simple Proofs for Bochner-Schoenberg-Eberlein and the Bochner-Schoenberg-Eberlein Module Properties on ℓpX,A |
| title_sort | simple proofs for bochner schoenberg eberlein and the bochner schoenberg eberlein module properties on lpx a |
| url | http://dx.doi.org/10.1155/2024/5893357 |
| work_keys_str_mv | AT shirintavkoli simpleproofsforbochnerschoenbergeberleinandthebochnerschoenbergeberleinmodulepropertiesonlpxa AT rasoulabazari simpleproofsforbochnerschoenbergeberleinandthebochnerschoenbergeberleinmodulepropertiesonlpxa AT alijabbari simpleproofsforbochnerschoenbergeberleinandthebochnerschoenbergeberleinmodulepropertiesonlpxa |