{"paper":{"title":"The order topology on duals of C$^\\ast$-algebras and von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Emmanuel Chetcuti, Jan Hamhalter","submitted_at":"2018-12-10T19:21:20Z","abstract_excerpt":"For a von Neumann algebra $\\mathcal M$ we study the order topology associated with the hermitian part $\\mathcal M_*^s$ and to intervals of the predual $\\mathcal M_*$. It is shown that the order topology on $\\mathcal M_*^s$ coincides with the topology induced by the norm. In contrast to this, it is proved that the condition of having the order topology associated to the interval $[0,\\varphi]$ equal to that induced by the norm for every $\\varphi\\in \\mathcal M_*^+$, is necessary and sufficient for the commutativity of $\\mathcal M$. It is also proved that if $\\varphi$ is a positive bounded linear "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04035","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"}