{"paper":{"title":"Dominated Uryson operators on lattice-normed spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Batradz Tasoev, Marat Pliev","submitted_at":"2013-09-24T08:13:42Z","abstract_excerpt":"The aim of this note is to introduce the space D_{U}(V,W) of the dominated Uryson operators on lattice-normed spaces. We prove an \"Up-and-down\" type theorem for a positive abstract Uryson operator defined on a vector lattice and taking values in a Dedekind complete vector lattice. This result we apply to prove the decomposability of the lattice valued norm of the space D_{U}(V,W) of all dominated Uryson operators. We obtain that, for a lattice-normed space V and a Banach-Kantorovich space W the space D_{U}(V,W) is also a Banach-Kantorovich space. We prove that under some mild conditions, a dom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6074","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"}