Compact Operators for Almost Conservative and Strongly Conservative Matrices

Abstract

We obtain the necessary and sufficient conditions for an almost conservative matrix to define a compact operator. We also establish some necessary and sufficient (or only sufficient) conditions for operators to be compact for matrix classes $(f,X)$, where $X=c,c_0,l_{\infty }$. These results are achieved by applying the Hausdorff measure of noncompactness.