A study on Copson operator and its associated sequence space II

[摘要] 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.

[学科分类] 电力

[关键词] Sequence space;Lower bound;Copson matrix;Hausdorff matrix;Hilbert matrix