Hausdorff measure of noncompactness in some sequence spaces of a triple band matrix

The sequence spaces c0(B), ℓ∞(B) have recently been introduced by Sömez (Comput. Math. Appl. 62:641-650, 2011). In this paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the spaces c0(B), ℓ∞(B) and by using the Hausdorff measure of noncompactness, we characterize some classes of compact operators on these spaces.