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), whereX=c,c0,l∞. These results are achieved by applying the Hausdorff measure of noncompactness.

Erratum to “Compact Operators for Almost Conservative and Strongly Conservative Matrices”

“…An infinite matrix = ( ) ∞ , =1 is said to be Bstrongly conservative if ∈ for all ∈ , and we denote it by ∈ ( , ). Now, we restate Theorem 11 and Theorem 15 of [1] as follows, respectively.…”