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On the structure of duals in paranormed sequence spaces of quaternions |
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| รหัสดีโอไอ | |
| Creator | Qing-Bo Cai |
| Title | On the structure of duals in paranormed sequence spaces of quaternions |
| Contributor | Omer Kisi, Mehmet Gurdal |
| Publisher | Maejo University |
| Publication Year | 2569 |
| Journal Title | Maejo International Journal of Science and Technology |
| Journal Vol. | 20 |
| Journal No. | 2 |
| Page no. | 184 |
| Keyword | paranormed sequence spaces, quaternion space, quaternion numbers, a-dual, b-dual, y-dual |
| Website title | Maejo International Journal of Science and Technology |
| ISSN | 1905-7873 |
| Abstract | This study develops a duality theory for paranormed sequence spaces whose terms take values in the non-commutative algebra of quaternions. Starting from Maddox-type positive exponent sequences, we introduce quaternion-valued analogues of the bounded, convergent, null and p-absolutely summable sequence classes. We then determine the corresponding a-, b- and y-duals of these spaces. The main novelty of the study is that the duality problem is not treated as a direct scalar-field replacement of the classical real or complex case. Instead, the non-commutativity of quaternion multiplication is explicitly incorporated into the structure of the dual spaces. In particular, the convergence and boundedness conditions appearing in the definitions of the b- and y-duals require a distinction between left and right multiplication, a phenomenon absent from classical sequence-space theory over commutative scalar fields. The obtained results extend Maddox-type paranormed sequence-space duality to the quaternionic setting and clarify the joint role of the paranorm topology and the order of quaternionic multiplication. |
