{"paper":{"title":"Characterizations of centralizable mappings 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, Jiankui Li, Jun He","submitted_at":"2018-09-13T11:05:53Z","abstract_excerpt":"A linear mapping $\\phi$ from an algebra $\\mathcal{A}$ into its bimodule $\\mathcal M$ is called a centralizable mapping at $G\\in\\mathcal{A}$ if $\\phi(AB)=\\phi(A)B=A\\phi(B)$ for each $A$ and $B$ in $\\mathcal{A}$ with $AB=G$. In this paper, we prove that if $\\mathcal M$ is a von Neumann algebra without direct summands of type $\\mathrm{I}_1$ and type $\\mathrm{II}$, $\\mathcal A$ is a $*$-subalgebra with $\\mathcal M\\subseteq\\mathcal A\\subseteq LS(\\mathcal{M})$ and $G$ is a fixed element in $\\mathcal A$, then every continuous (with respect to the local measure topology $t(\\mathcal M)$) centralizable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04887","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"}