On Some Euler Sequence Spaces of Nonabsolute Type

  • B. Altay
  • F. Başar

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 $1 \leq p \leq \infty$.
Published
25.01.2005
How to Cite
AltayB., and BaşarF. “On Some Euler Sequence Spaces of Nonabsolute Type”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 1, Jan. 2005, pp. 3–17, https://umj.imath.kiev.ua/index.php/umj/article/view/3570.
Section
Research articles