Sequence spaces of a double sequential band matrix and the Hausdorff measure of noncompactness

The paranormed sequence spaces l ∞ (˜B, p), c(˜B , p), and c0(˜B, p) have recently been defined. These sequence spaces are of non-absolute type derived by the double sequential band matrix B(˜r, ˜s). In this work, we establish identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on these spaces. The main purpose of this work is to find the necessary and sufficient condition for compactness of LA in the class (X, l∞ (q)) (where X is any of the spaces l∞ (˜B, p), c(˜B , p) or c0(˜B, p)) and characterize some classes of compact operators on these spaces by applying the Hausdorff measure of the noncompactness technique.