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

Abstract

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

Keywords

• Sequence spaces
• Cesàro matrix
• Copson matrix
• Copson matrix of order α
• Matrix transformations
• Hausdorff measure of noncompactness