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Zbl 1201.40001
Kirişçi, Murat; Başar, Feyzi
Some new sequence spaces derived by the domain of generalized difference matrix.
(English)
[J] Comput. Math. Appl. 60, No. 5, 1299-1309 (2010). ISSN 0898-1221

Summary: Let $\lambda$ denote any one of the classical spaces $\ell \infty , c, c_{0}$ and $\ell p$ of bounded, convergent, null and absolutely $p$-summable sequences, respectively, and $\hat{\lambda}$ also be the domain of the generalized difference matrix $B(r,s)$ in the sequence space $\lambda$, where $1\leq p<\infty$. The present paper is devoted to studying on the sequence space $\hat{\lambda}$. Furthermore, the $\beta$- and $\gamma$-duals of the space $\hat{\lambda}$ are determined, and the Schauder bases for the spaces $\hat{c_0}$, $\hat{\ell_1}$ and $\hat{\ell_p}$ are given, and some topological properties of the spaces $\hat{c_0}$, $\hat{\ell_1}$ and $\hat{\ell_p}$ are examined. Finally, the classes $\hat{\lambda_1:\lambda_2}$ and $\hat{\lambda}_1:\hat{\lambda}_2$ 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
46A45 Sequence spaces

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

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