On domain of Nörlund matrix
Summary: In 1978, the domain of the Nörlund matrix on the classical sequence spaces \(l_p\) and \(l_\infty\) was introduced by \textit{C.-S Wang}, Tamkang J. Math. 9, 269--274 (1979; Zbl 0415.46009), where \(1\leq p<\infty\). \textit{O. Tuğ} and \textit{F. Başar} studied the matrix domain of Nörlund mean on the sequence spaces \(f_0\) and \(f\) in [Filomat 30, No.~3, 773--783 (2016; Zbl 1462.46009)]. Additionally, \textit{O. Tuğ} defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in [Eurasian J. Sci. Eng. 3, No. 2, 111--120 (2017; \url{doi:10.23918/eajse.v3i2p111})]. In this article, we define the new spaces \(b s(N^t)\) and \(c s(N^t)\) and examine the domain of the Nörlund mean on \(bs\) and \(cs\), which are bounded and convergent series, respectively. We also examine their inclusion relations. We define norms over them and investigate whether these new spaces are Banach spaces. Finally, we determine their \(\alpha\)-, \(\beta\)-, \(\gamma\)-duals, and characterize the matrix transformations on and into this space.
scientific article; zbMATH DE number 6994871
scientific article