In a previous paper the author studied the compactness of multiplication, composition and weighted composition operators among some sequence spaces. We were motivated by these results and present two different approaches for obtaining some of the results in a previous paper. The first approach is to apply the theory of matrix transformations and the Hausdorff measure of noncompactness, and the second one is to use known results on multiplier spaces and the Hausdorff measure of noncompactness. We also use our techniques and methods from our proofs of the existing results to establish some new results related to the class of Fredholm operators and some classes of operators considered here and in the previous paper.
"Compactness of multiplication, composition and weighted composition operators between some classical sequence spaces: A new approach." Rocky Mountain J. Math. 47 (8) 2545 - 2564, 2017. https://doi.org/10.1216/RMJ-2017-47-8-2545