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

We establish the characterisations of classes bounded linear operators from generalised Hahn sequence space hd, where d is an unbounded monotone increasing positive real numbers, into spaces w0, w and w? sequences that are strongly summable to zero, by Ces?ro method order one. Furthermore, we prove estimates for Hausdorff measure noncompactness hd w, identities use these results characterise compact w0. Finally, provide example application our results.