# On matrix operators on the series space $|\bar{N}_p^θ|_k$

### Abstract

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.
Published

25.11.2017

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 69, no. 11, Nov. 2017, pp. 1524-33, http://umj.imath.kiev.ua/index.php/umj/article/view/1800.

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Section

Research articles