Generalized Difference Spaces of Non-Absolute Type of Convergent and Null Sequences

Abstract

The aim of the present paper is to introduce the spaces $c_0^{\lambda }(B)$ and $c^{\lambda }(B)$ of generalized difference sequences which generalize the paper due to Mursaleen and Noman (2010). These spaces are the BK-spaces of non-absolute type and norm isomorphic to the spaces $c_0$ and $c$, respectively. Furthermore, we derive some inclusion relations determine the $\alpha \text{-}$, $\beta \text{-}$, and $\gamma \text{-}$duals of those spaces, and construct their Schauder bases. Finally, we characterize some matrix classes from the spaces $c_0^{\lambda }(B)$, and $c^{\lambda }(B)$ to the spaces ${\ell }_p$, $c_0$, and c.