On the spaces of Cesàro absolutely p‐summable, null, and convergent sequences

Abstract

In this paper, we investigate some properties of the domains c0(Cn), c(Cn), and ℓp(Cn) with 0 < p < 1 of the Cesàro matrix of order n in the classical spaces c0, c, and ℓp of null, convergent, and absolutely p‐summable sequences, respectively, and compute the α‐, β‐, and γ‐duals of these spaces. We characterize the classes of infinite matrices from the space ℓp(Cn) to the spaces ℓ∞, c, and c0 and from a normed sequence spaces to the sequence spaces c0(Cn), c(Cn), and ℓp(Cn). Moreover, we compute the lower bound of operators from ℓp into ℓp(Cn), from ℓp(Cn) into ℓp and from ℓp(Cn) into itself.