TY - JOUR
AU - R. N. Mohapatra
AU - M. A. Sarigol
PY - 2017/11/25
Y2 - 2024/08/03
TI - On matrix operators on the series space $|\bar{N}_p^θ|_k$
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 69
IS - 11
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1800
AB - 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 $\beta$ -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.
ER -