Some paranormed sequence spaces of non-absolute type derived by weighted mean |
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Authors: | Bilâ l Altay |
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Affiliation: | ?nönü Üniversitesi, E?itim Fakültesi, Malatya 44280, Turkey |
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Abstract: | The sequence spaces ?∞(p), c(p) and c0(p) were introduced and studied by Maddox [I.J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Cambridge Philos. Soc. 64 (1968) 335-340]. In the present paper, the sequence spaces λ(u,v;p) of non-absolute type which are derived by the generalized weighted mean are defined and proved that the spaces λ(u,v;p) and λ(p) are linearly isomorphic, where λ denotes the one of the sequence spaces ?∞, c or c0. Besides this, the β- and γ-duals of the spaces λ(u,v;p) are computed and the basis of the spaces c0(u,v;p) and c(u,v;p) is constructed. Additionally, it is established that the sequence space c0(u,v) has AD property and given the f-dual of the space c0(u,v;p). Finally, the matrix mappings from the sequence spaces λ(u,v;p) to the sequence space μ and from the sequence space μ to the sequence spaces λ(u,v;p) are characterized. |
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Keywords: | Paranormed sequence space f-, β- and γ-duals Weighted mean AD property and matrix mappings |
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