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Zbl 1228.40006
Sönmez, Abdulcabbar
Some new sequence spaces derived by the domain of the triple band matrix. (English)
[J] Comput. Math. Appl. 62, No. 2, 641-650 (2011). ISSN 0898-1221

Summary: Let $\lambda $ denote any of the classical spaces $\ell_{\infty },c,c_{0}$, and $\ell _{p}$ of bounded, convergent, null, and absolutely $p$-summable sequences, respectively, and let $\lambda (B)$ also be the domain of the triple band matrix $B(r,s,t)$ in the sequence space $\lambda $, where $1<p<\infty$. The present paper is devoted to studying the sequence space $\lambda (B)$. Furthermore, the $\beta $- and $\gamma $-duals of the space $\lambda (B)$ are determined, the Schauder bases for the spaces $c(B), c_{0}(B)$, and $\ell _{p}(B)$ are given, and some topological properties of the spaces $c_{0}(B), \ell _{1}(B)$, and $\ell _{p}(B)$ are examined. Finally, the classes $(\lambda _{1}(B):\lambda _{2})$ and $(\lambda _{1}(B):\lambda _{2}(B))$ of infinite matrices are characterized, where $\lambda _{1}\in {\ell _{\infty },c,c_{0},\ell _{p},\ell _{1}}$ and $\lambda _{2}\in {\ell _{\infty },c,c_{0},\ell _{1}}$.

MSC 2000:: *40C05 Matrix methods in summability
40H05 Functional analytic methods in summability
46B45 Banach sequence spaces

Keywords: matrix domain of a sequence space; Schauder basis; $\beta $- and $\gamma $-duals and matrix transformations

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