{"paper":{"title":"Relatively Uniformly Continuous Semigroups on Vector Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marko Kandi\\'c, Michael Kaplin","submitted_at":"2018-07-06T18:42:16Z","abstract_excerpt":"In this paper we study continuous semigroups of positive operators on general vector lattices equipped with the relative uniform topology $\\tau_{ru}$. We introduce the notions of strong continuity with respect to $\\tau_{ru}$ and relative uniform continuity for semigroups. These notions allow us to study semigroups on non-locally convex spaces such as $L^p(\\mathbb{R})$ for $0<p<1$ and non-complete spaces such as $Lip(\\mathbb{R})$, $UC(\\mathbb{R})$, and $C_c(\\mathbb{R})$. We show that the (left) translation semigroup on the real line, the heat semigroup and some Koopman semigroups are relatively"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02543","kind":"arxiv","version":2},"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"}