2018
Том 70
№ 12

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 $1 \leq p \leq \infty$.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 1, pp 1-17.

Citation Example: Altay B., Başar F. On Some Euler Sequence Spaces of Nonabsolute Type // Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 3–17.

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