On Some Sequence Spaces of Non-Absolute Type

Sinan Ercan, Ciğdem A. Bektaş

In this paper, we introduce the notion of $\lambda_{v}$-convergent and bounded sequences. Further, we introduce the spaces $\ell_{\infty}^{\lambda}\left( \triangle_{v}\right)$, $c_{0}^{\lambda} \left(\triangle_{v}\right)$ and $c^{\lambda} \left( \triangle_{v} \right)$, which are BK-spaces of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces $\ell_{\infty}$, $c_{0}$ and $c$, respectively. Moreover, we establish some inclusion relations between these spaces.