Compact operators on sequence spaces associated with the Copson matrix of order α

In this work, we study characterizations of some matrix classes $(\mathcal{C}^{(\alpha )}(\ell ^{p}),\ell ^{\infty })$ ( C ( α ) ( ℓ p ) , ℓ ∞ ) , $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c)$ ( C ( α ) ( ℓ p ) , c ) , and $(\mathcal{C}^{(\alpha )}(\ell ^{p}),c^{0})$ ( C ( α ) ( ℓ p ) , c 0 ) , where $\mathcal{C}^{(\alpha )}(\ell ^{p})$ C ( α ) ( ℓ p ) is the domain of Copson matrix of order α in the space $\ell ^{p}$ ℓ p ($0< p<1$ 0 < p < 1 ). Further, we apply the Hausdorff measures of noncompactness to characterize compact operators associated with these matrices.