On Some Euler Sequence Spaces of Nonabsolute Type
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, so...
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| Date: | 2005 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2005
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3570 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 $1 \leq p \leq \infty$. |
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