Compactness by the Hausdorff measure of noncompactness

In the present paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators given by infinite matrices that map an arbitrary BKBK-space into the sequence spaces c0c0, cc, ℓ∞ℓ∞ and ℓ1ℓ1, and into the matrix domains of triangles in these spaces. Furthermore, by using the Hausdorff measure of noncompactness, we apply our results to characterize some classes of compact operators on the BKBK-spaces.