2019
Том 71
№ 6

All Issues

Mohapatra R. N.

Articles: 1
Article (English)

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

Mohapatra R. N., Sarigol M. A.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 11. - pp. 1524-1533

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.