BOUNDED LINEAR AND COMPACT OPERATORS BETWEEN THE HAHN SPACE AND SPACES OF STRONGLY SUMMABLE AND BOUNDED SEQUENCES

We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space hd, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces ω 0 p , wp and ω ∞ p of sequences that are strongly summable to zero, strongly summable and strongly bounded by the Cesàro method of order one and index p for 1 ≤ p < ∞. Furthermore, we prove estimates for the Hausdorff measure of noncompactness of bounded linear operators from hd into wp, and identities for the Hausdorff measure of noncompactness of bounded linear operators from hd to ω 0 p . We use these results to characterise the classes of compact operators from hd to wp and ω 0 p . Finally, we provide an example for some applications of our results and visualisations in crystallography.