Characterisations of bounded linear and compact operators on the generalised Hahn space-Reference-Cited by-同舟云学术

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

Published:2022 Issue:2 Volume:36 Page:497-505
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Dolicanin-Djekic Diana¹^ORCID,Gilic Ersin²

Affiliation:

1. University of Priština in Kosovska Mitrovica, Faculty of Technical Sciences, Department of Mathematics and Phisics, Kosovska Mitrovica, Serbia

2. State University of Novi Pazar, Department of Mathematics, Novi Pazar, Serbia

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 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.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference30 articles.

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