The measure of noncompactness of linear operators between spaces of \(M^{th}\)-order difference sequences (Q2714351)

In this paper we investigate linear operators between certain sequence spaces \(X\) and \(Y\). Among other things, if \(X\) is any BK space and \(Y\) is a sequence space of bounded or convergent \(M^{\text{th}}\)-order differences, then we find necessary and sufficient conditions for infinite matrices \(A\) to map \(X\) into \(Y\). Further the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for \(A\) to be a compact operator.