On matrix operators on the series space $|\bar{N}_p^θ|_k$ - Mohapatra, R. N.; Sarigol, M. A. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
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 seriessummable by the absolute weighted method. In the paper, we investigate some properties of this space, such as $β$ -dualityand 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, wededuce some well-known results of Sarıg¨ol, Bosanquet, Orhan, and Sunouchi.