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Generalization of the sequence space $\ell (p)$ derived by weighted mean. (English) Zbl 1116.46003
Summary: The sequence space $\ell(p)$ was introduced and studied by {\it I. J.\thinspace Maddox} [Q. J. Math., Oxf., II. Ser. 18, 345--355 (1967; Zbl 0156.06602)]. In the present paper, the sequence spaces $\ell(u,v;p)$ of non-absolute type which are derived by the generalized weighted mean are defined and it is proved that the spaces $\ell(u,v;p)$ and $\ell(p)$ are linearly isomorphic. Besides this, the $\beta$- and $\gamma$-duals of the space $\ell(u,v;p)$ are computed and a basis of that space is constructed. Further, it is established that the sequence space $\ell_p(u,v)$ has the AD property and the $f$-dual of the space $\ell_p (u,v)$ is given. Finally, the matrix mappings from the sequence spaces $\ell(u,v;p)$ to the sequence space $\mu$ and from the sequence space $\mu$ to the sequence space $\ell(u,v;p)$ are characterized.

MSC:
46A45Sequence spaces
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References:
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