{"paper":{"title":"Unbounded $\\sigma$-order-to-norm continuous and $un$-continuous operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kazem Haghnejad Azar, Mina Matin, Razi Alavizadeh","submitted_at":"2019-08-08T17:55:07Z","abstract_excerpt":"An operator $T $ from a vector lattice $E$ into a normed lattice $F$ is called unbounded $\\sigma$-order-to-norm continuous whenever $x_{n}\\xrightarrow{uo}0$ implies $\\| Tx_{n}\\|\\rightarrow 0$, for each sequence $(x_{n})_n\\subseteq E$. For a net $(x_{\\alpha})_{\\alpha}\\subseteq E$, if $x_{\\alpha}\\xrightarrow{un}0$ implies $Tx_{\\alpha}\\xrightarrow{un}0$, then $T$ is called an unbounded norm continuous operator.\n  In this manuscript, we study some properties of these classes of operators and their relationships with the other classes of operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03192","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03192/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}