On the Paranormed Nörlund Sequence Space of Nonabsolute Type
Maddox defined the space ℓ(p) of the sequences x=(xk) such that ∑k=0∞|xk|pk<∞, in Maddox, 1967. In the present paper, the Nörlund sequence space Nt(p) of nonabsolute type is introduced and proved that the spaces Nt(p) and ℓ(p) are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-d...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/858704 |
| Summary: | Maddox defined the space ℓ(p) of the sequences x=(xk) such that ∑k=0∞|xk|pk<∞, in Maddox, 1967. In the present paper, the Nörlund sequence space Nt(p) of nonabsolute type is introduced and proved that the spaces Nt(p) and ℓ(p) are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-duals of the space Nt(p) are computed and the basis of the space Nt(p) is constructed. The classes (Nt(p):μ) and (μ:Nt(p)) of infinite matrices are characterized. Finally, some geometric properties of the space Nt(p) are investigated. |
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| ISSN: | 1085-3375 1687-0409 |