{"paper":{"title":"Strongly order continuous operators on Riesz spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Akbar Bahramnezhad, Kazem Haghnejad Azar","submitted_at":"2017-12-12T13:08:57Z","abstract_excerpt":"In this paper we introduce two new classes of operators that we call strongly order continuous and strongly $\\sigma$-order continuous operators. An operator $T:E\\rightarrow F$ between two Riesz spaces is said to be strongly order continuous (resp. strongly $\\sigma$-order continuous), if $x _\\alpha \\xrightarrow{uo}0$ (resp. $x _n \\xrightarrow{uo}0$) in $E$ implies $Tx _\\alpha \\xrightarrow{o}0$ (resp. $Tx _n \\xrightarrow{o}0$) in $F$. We give some conditions under which order continuity will be equivalent to strongly order continuity of operators on Riesz spaces. We show that the collection of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04275","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}