Abstract
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.
Highlights
Let ω denote the set of all real-valued sequences
For 0 < p < 1, the complete p-normed space p is the set of all real sequences x =∞ k=0 ∈ ω such that
3.1 Lower bound of operators from p into p(Cn) In this part of study we intend to compute the lower bound of transposed Hausdorff operators on the Copson matrix domain
Summary
Let ω denote the set of all real-valued sequences. Any linear subspace of ω is called a sequence space. The author have investigated the sequence space p(Cn) for 1 ≤ p < ∞, as well as found the norm of well-known operators on this matrix domain. 3.1 Lower bound of operators from p into p(Cn) In this part of study we intend to compute the lower bound of transposed Hausdorff operators on the Copson matrix domain.
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