{"paper":{"title":"Characterizations of Jordan derivations on algebras of locally measurable operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guangyu An, Jun He","submitted_at":"2018-03-06T07:48:29Z","abstract_excerpt":"We prove that if $\\mathcal M$ is a properly infinite von Neumann algebra and $LS(\\mathcal M)$ is the local measurable operator algebra affiliated with $\\mathcal M$, then every Jordan derivation from $LS(\\mathcal M)$ into itself is continuous with respect to the local measure topology $t(\\mathcal M)$. We construct an extension of a Jordan derivation from $\\mathcal M$ into $LS(\\mathcal M)$ up to a Jordan derivation from $LS(\\mathcal M)$ into itself. Moreover, we prove that if $\\mathcal M$ is a properly von Neumann algebra and $\\mathcal A$ is a subalgebra of $LS(\\mathcal M)$ such that $\\mathcal M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02050","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"}