Open AccessCharacterisations of bounded linear and compact operators on the generalised Hahn space
Author(s) -
Diana Dolicanin-Djekic,
Ersin Gilić
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202497d
Subject(s) - bounded function , mathematics , hausdorff measure , sequence (biology) , hausdorff space , measure (data warehouse) , monotone polygon , bounded operator , hausdorff distance , linear operators , space (punctuation) , pure mathematics , zero (linguistics) , discrete mathematics , mathematical analysis , hausdorff dimension , linguistics , philosophy , geometry , database , biology , computer science , genetics
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 w? of sequences that are strongly summable to zero, strongly summable and strongly bounded by the Ces?ro method of order one. Furthermore, we prove estimates for the Hausdorff measure of noncompactness of bounded linear operators from hd into w, and identities for the Hausdorff 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.