In this paper, we investigate some properties of the domains $c(C^{n})$ , $c_{0}(C^{n})$ , and $\ell _{p}(C^{n})$ $(0< p<1)$ of the Copson matrix of order n, where c, $c_{0}$ , and $\ell _{p}$ are the spaces of all convergent, convergent to zero, and p-summable real sequences, respectively. Moreover, we compute the Köthe duals of these spaces and the lower bound of well-known operators on these sequence spaces. The domain $\ell _{p}(C^{n})$ of Copson matrix $C^{n}$ of order n in the sequence space $\ell _{p}$ , the norm of operators on this space, and the norm of Copson operator on several matrix domains have been investigated recently in (Roopaei in J. Inequal. Appl. 2020:120, 2020), and the present study is a complement of our previous research.

中文翻译：

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Copson算子及其相关序列空间的研究

在本文中，我们研究了域$ c（C ^ {n}）$，$ c_ {0}（C ^ {n}）$和$ \ ell _ {p}（C ^ {n} } $ $（0 <p <1）$阶n的Copson矩阵，其中c，$ c_ {0} $和$ \ ell _ {p} $是所有会聚的空间，会聚为零，并且p可加实数序列。此外，我们计算这些空间的Köthe对偶以及这些序列空间上知名算子的下界。序列空间$ \ ell _ {p} $中的阶次n的Copson矩阵$ C ^ {n} $的域$ \ ell _ {p}（C ^ {n}）$，在该空间上的算子范数，最近在（Roopaei in J. Inequal。Appl。2020：120，2020）中研究了Copson算子在几个矩阵域上的范数，并且本研究是对我们先前研究的补充。