In this research, we investigate two types of Copson matrices, the generalized Copson matrix and the Copson matrix of order n, and their associated sequence spaces generated by these matrices. We also investigate the topological properties, inclusions, and dual spaces of these new Banach spaces as well as compute the norm of Copson operators on the well-known matrix domains such as Hilbert and difference sequence spaces. Moreover, in a reverse manner, we investigate the norm of well-known operators on the Copson matrix domains generated with Copson matrices. Through this study we introduce several new inequalities, inclusions, and factorizations for well-known operators.

中文翻译：

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Copson算子及其相关序列空间的研究

在这项研究中，我们研究了两种类型的Copson矩阵，即广义Copson矩阵和n阶Copson矩阵，以及这些矩阵所生成的相关序列空间。我们还研究了这些新Banach空间的拓扑性质，包含和对偶空间，并计算了Hilbert和差分序列空间等著名矩阵域上Copson算子的范数。此外，以相反的方式，我们研究了用Copson矩阵生成的Copson矩阵域上的著名算子的范数。通过这项研究，我们为知名算子引入了几个新的不等式，包含和因式分解。