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Zbl 1201.40003
Mursaleen, M.; Noman, Abdullah K.
On some new difference sequence spaces of non-absolute type. (English)
[J] Math. Comput. Modelling 52, No. 3-4, 603-617 (2010). ISSN 0895-7177

Summary: We introduce the spaces $c_0^{\lambda}(\Delta)$ and $c^{\lambda}(\Delta)$ of difference sequences which are the $BK$-spaces of non-absolute type and prove that these spaces are linearly isomorphic to the spaces $c_{0}$ and $c$, respectively. We also derive some inclusion relations. Furthermore, we determine the $\alpha -, \beta $- and $\gamma $-duals of those spaces and construct their bases. Finally, we characterize some matrix classes concerning the spaces $c_0^{\lambda}(\Delta)$ and $c^{\lambda}(\Delta)$.

MSC 2000:: *40C05 Matrix methods in summability

Keywords: sequence spaces; Schauder basis; $\alpha; \beta $- and $\gamma $-duals; matrix transformations

Cited in: Zbl 1231.47029

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