Some paranormed sequence spaces of non-absolute type derived by weighted mean

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. © 2005 Elsevier Inc. All rights reserved.