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On some new difference sequence spaces of non-absolute type. (English) Zbl 1201.40003
Summary: We introduce the spaces ${c}_{0}^{\lambda }\left({\Delta }\right)$ and ${c}^{\lambda }\left({\Delta }\right)$ 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 ${c}_{0}^{\lambda }\left({\Delta }\right)$ and ${c}^{\lambda }\left({\Delta }\right)$.

##### MSC:
 40C05 Matrix methods in summability