On matrix operators on the series space $|\bar{N}_p^θ|_k$
Recently, the space $|\bar{N}_p^θ|_k$ has been generated from the set of $k$-absolutely convergent series $\ell_k$ as the set of series summable by the absolute weighted method. In the paper, we investigate some properties of this space, such as $\beta$ -duality and the relationship with \ell k and...
Збережено в:
| Дата: | 2017 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2017
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1800 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | Recently, the space $|\bar{N}_p^θ|_k$
has been generated from the set of $k$-absolutely convergent series $\ell_k$ as the set of series
summable by the absolute weighted method. In the paper, we investigate some properties of this space, such as $\beta$ -duality
and the relationship with \ell k and then show that each element in the classes
$\Bigl(|\bar{N}_p|,\;|\bar{N}_p^θ|_k\Bigr)$
and
$\Bigl(|\bar{N}_p^θ|_k,\;|\bar{N}_q|\Bigr)$
of infinite matrices corresponds to a continuous linear operator and also characterizes these classes. Hence, in the special case, we
deduce some well-known results of Sarıg¨ol, Bosanquet, Orhan, and Sunouchi. |
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