On Sums of Strictly Narrow Operators Acting from a Riesz Space to a Banach Space. (2nd June 2019)

• Record Type: Journal Article
• Authors: Maslyuchenko, Oleksandr; Popov, Mikhail
• Other Names: Martin Miguel Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2019(2019)
• Publication Date: 2019-06-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2019/8569409
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We prove that ifE is a Dedekind complete atomless Riesz space andX is a Banach space, then the sum of two laterally continuous orthogonally additive operators fromE toX, one of which is strictly narrow and the other one is hereditarily strictly narrow with finite variation (in particular, has finite rank), is strictly narrow. Similar results were previously obtained for narrow operators by different authors; however, no theorem of the kind was known for strictly narrow operators.