In recent years, the space \( {\left|{\overline{N}}_p^{\theta}\right|}_k \) has been generated from the set of k -absolutely convergent series ℓ k as the set of series summable by the absolute weighted method. We investigate some properties of this space, such as β -duality and the relationship with ℓ k and then show that each element in the classes \( \left(\left|{\overline{N}}_p\right|,{\left|{\overline{N}}_q^{\theta}\right|}_k\right) \) and \( \left({\left|{\overline{N}}_p^{\theta}\right|}_k,\left|{\overline{N}}_q\right|\right) \) of infinite matrices corresponds to a continuous linear operator and also characterizes these classes. Hence, in a special case, we deduce some well-known results of Sarıgöl, Bosanquet, Orhan, and Sunouchi.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 11, pp. 1524–1533, November, 2017.
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Mohapatra, R.N., Sarıgöl, M.A. On Matrix Operators on the Series Space \( {\left|{\overline{N}}_p^{\theta}\right|}_k \). Ukr Math J 69, 1772–1783 (2018). https://doi.org/10.1007/s11253-018-1469-0
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DOI: https://doi.org/10.1007/s11253-018-1469-0