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

In this paper, we investigate some properties of the domains c 0 ( C n ) , c ( C n ) , and ℓ p ( C n ) with 0 <  p  < 1 of the Cesàro matrix of order n in the classical spaces c 0 , c , and ℓ p 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 ℓ p ( C n ) to the spaces ℓ ∞ , c , and c 0 and from a normed sequence spaces to the sequence spaces c 0 ( C n ) , c ( C n ) , and ℓ p ( C n ) . Moreover, we compute the lower bound of operators from ℓ p into ℓ p ( C n ) , from ℓ p ( C n ) into ℓ p and from ℓ p ( C n ) into itself.