Compact operators on spaces of sequences of weighted means

We reduce the spaces a₀^r, a_c^r, a₀^r (Δ) and a_c^r (Δ) and simplify their dual spaces and the characterisations of matrix transformations on them. We also obtain an estimate and a formula for the Hausdorff measure of noncompactness of some matrix operators on the spaces a₀^r and a_c^r and the corresponding characterisations of compact matrix operators.