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Zbl 1105.46005
Altay, Bilâl; Başar, Feyzi
Some paranormed sequence spaces of non-absolute type derived by weighted mean. (English)
[J] J. Math. Anal. Appl. 319, No. 2, 494-508 (2006). ISSN 0022-247X

Summary: The sequence spaces $\ell_\infty(p)$, $c(p)$ and $c_0(p)$ were introduced and studied by {\it I.~J.\ Maddox}, Proc.\ Camb.\ Philos.\ Soc.\ 64, 335--340 (1968; Zbl 0157.43503)]. In the present paper, the sequence spaces $\lambda(u,v;p)$ of non-absolute type which are derived by the generalized weighted mean are defined and it is proved that the spaces $\lambda(u,v;p)$ and $\lambda(p)$ are linearly isomorphic, where $\lambda$ denotes one of the sequence spaces $\ell_\infty$, $c$ or $c_0$. Besides this, the $\beta$- and $\gamma$-duals of the spaces $\lambda(u,v;p)$ are computed and basis of the spaces $c_0(u,v;p)$ and $c(u,v;p)$ is constructed. Additionally, it is established that the sequence space $c_0(u,v)$ has the AD property and the $f$-dual of the space $c_0(u,v;p)$ is given. Finally, the matrix mappings from the sequence spaces $\lambda(u,v;p)$ to the sequence space $\mu$ and from the sequence space $\mu$ to the sequence spaces $\lambda(u,v;p)$ are characterized.

MSC 2000:: *46A45 Sequence spaces

Keywords: paranormed sequence space; $f$-, $\beta$- and $\gamma $-duals; weighted mean; AD property; matrix mappings

Citations: Zbl 0157.43503

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