Compact and matrix operators on the space |C,-1| k

According to Hardy [5], Cesàro summability is usually considered for the range α ≥ -1: In a more recent paper [14], the space |C α | k is studied for α ≥ -1: In this paper we de.ne |C -1 | k using the Cesàro mean (C, -1) of Thorpe [26], compute its α-, β- and γ- duals, give some algebraic and topological properties, and characterize related matrix operators, and also obtain some identities or estimates for the their operator norms and the Hausdorff measure of noncompactness. Further, by applying the Hausdorff measure of noncompactness, we establish the necessary and sufficient conditions for such operators to be compact. So some results in [14] is also extended to the range α ≥ -1. © 2018 by Eudoxus Press, LLC. All rights reserved