On Some Euler Sequence Spaces of Nonabsolute Type

Abstract

In the present paper, the Euler sequence spaces $e_0^r$ and $e^r_c$ of nonabsolute type which are the $BK$-spaces including the spaces $c_0$ and $c$ have been introduced and proved that the spaces $e_0^r$ and $e^r_c$ are linearly i somorphic to the spaces $c_0$ and $c$, respectively. Furthemore, some inclusion theorems have been given. Additionally, the $\alpha-, \beta-, \gamma-$ and continuous duals of the spaces $e_0^r$ and $e^r_c$ have been computed and their basis have been constructed. Finally, the necessary and sufficient conditions on an infinite matrix belonging to the classes $(e^r_c :\; {l}_p)$ and $(e^r_c :\; c)$ have been determined and the characterizations of some other classes of infinite matrices have also been derived by means of a given basic lemma, where $1 \leq p \leq \infty$.