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Zbl 1049.46002
Aydin, Cafer; Başar, Feyzi
Some new paranormed sequence spaces. (English)
[J] Inf. Sci. 160, No. 1-4, 27-40 (2004). ISSN 0020-0255

Summary: {\it I. J. Maddox} defined the sequence spaces $\ell_{\infty} (p), c(p)$ and $c_0(p)$ in [Proc. Camb. Philos. Soc. 64, 335--340 (1968; Zbl 0157.43503), Q. J. Math., Oxf. (2) 18, 345--355 (1967; Zbl 0156.06602)]. In the present paper, the sequence spaces $a_0^r(u,p)$ and $a_c^r(u,p)$ of non-absolute type are introduced and it is proved that the spaces $a_0^r(u,p)$ and $a_c^r(u,p)$ are linearly isomorphic to the spaces $c_0(p)$ and $c(p)$, respectively. Besides this, the $\alpha$-, $\beta$- and $\gamma$-duals of the spaces $a_0^r(u,p)$ and $a_c^r(u,p)$ are computed and their bases are constructed. Finally, a basic theorem is given and some matrix mappings from $a_0^r(u,p)$ to the sequence spaces of Maddox and to new sequence spaces are characterized.

MSC 2000:: *46A45 Sequence spaces

Keywords: paranormed sequence space; $\alpha$-dual; $\beta$-dual; $\gamma$-dual; basis of a sequence space; matrix mappings

Citations: Zbl 0157.43503; Zbl 0156.06602

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