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 hd, where d is an unbounded monotone increasing sequence of positive real numbers, into the spaces [c0], [c] and [c1] of sequences that are strongly convergent to zero, strongly convergent and strongly bounded. Furthermore, we prove estimates for the Hausdor_ measure of noncompactness of bounded linear operators from hd into [c], and identities for the Hausdor_ measure of noncompactness of bounded linear operators from hd to [c0], and use these results to characterise the classes of compact operators from hd to [c] and [c0].