Some Compact Operators on the Hahn Space

Abstract

We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space h_d, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces [c₀], [c] and [c_{\infty}] of sequences that are strongly convergent to zero, strongly convergent and strongly bounded. Furthermore, we prove estimates for the Hausdorff measure of noncompactness of bounded linear operators from h_d into [c], and identities for the Hausdorff measure of noncompactness of bounded linear operators from h_d to [c₀], and use these results to characterise the classes of compact operators from h_d to [c] and [c₀].