Open AccessSome Compact Operators on the Hahn Space
Author(s) -
Eberhard Malkowsky
Publication year - 2021
Language(s) - English
DOI - 10.52460/src.2021.001
Subject(s) - bounded function , mathematics , sequence (biology) , measure (data warehouse) , monotone polygon , bounded operator , zero (linguistics) , space (punctuation) , pure mathematics , linear operators , compact space , discrete mathematics , mathematical analysis , computer science , linguistics , philosophy , genetics , geometry , database , biology , operating system
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].