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 , where . These results are achieved by applying the Hausdorff measure of noncompactness.
S. A. Mohiuddine. M. Mursaleen. A. Alotaibi. "Compact Operators for Almost Conservative and Strongly Conservative Matrices." Abstr. Appl. Anal. 2014 (SI24) 1 - 6, 2014. https://doi.org/10.1155/2014/567317