On the spaces of $\lambda-$ convergent and bounded series

Abstract

The main purpose of this study is to introduce the spaces $cs^{\lambda}, cs_0^{\lambda}$ and $bs^{\lambda}$ which are $BK-$spaces of non-absolute type. We prove that these spaces are linearly isomorphic to the spaces $cs, cs_0$ and $bs$, respectively and derive some inclusion relations. Additionally, their Schauder bases have been constructed and the $\alpha-,\beta-$ and $\gamma-$ duals of these spaces have been computed. Finally, we characterize some matrix classes from the spaces $cs^{\lambda}, cs_0^{\lambda}$ and $bs^{\lambda}$ to spaces $\ell_p, c$ and $c_0$, where $1\leq p\leq\infty$ .