Hausdorff measure of noncompactness of matrix operators on some new difference sequence spaces

Abstract

Abstract The new sequence spaces X ( r , s , t ; Δ ) $X(r,s,t;\Delta)$ for X ∈ { l ∞ , c , c 0 } $X\in\{l_{\infty}, c, c_{0}\}$ have been defined by using generalized means and difference operator. In this work, we establish identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on some new difference sequence spaces X ( r , s , t ; Δ ) $X(r,s,t;\Delta )$ where X ∈ { l ∞ , c , c 0 , l p } $X\in\{l_{\infty}, c, c_{0},l_{p}\}$ ( 1 ≤ p < ∞ $1\leq{p}<\infty$ ), as derived by using generalized means. Further, we find the necessary and sufficient conditions for such operators to be compact by applying the Hausdorff measure of noncompactness. Finally, as applications we characterize some classes of compact operators between these new difference sequence spaces and some other BK-spaces.

Keywords

• sequence space
• difference operators
• matrix transformation
• generalized means
• compact operators
• Hausdorff measure of noncompactness