Characterisations of bounded linear and compact operators on the generalised Hahn space

Abstract

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 w0, w and w1 of sequences that are strongly summable to zero, strongly summable and
strongly bounded by the Ces`aro method of order one. Furthermore, we prove estimates for the Hausdor
measure of noncompactness of bounded linear operators from hd into w, and identities for the Hausdor
measure of noncompactness of bounded linear operators from hd to w0, and use these results to characterise
the classes of compact operators from hd to w and w0. Finally, we provide an example for an application of
our results.