{"paper":{"title":"Innerness of continuous 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":"A. F. Ber, F. A. Sukochev, V. I. Chilin","submitted_at":"2013-02-20T11:44:00Z","abstract_excerpt":"It is established that every derivation continuous with respect to the local measure topology acting on the *-algebra $LS(\\mathcal{M})$ of all locally measurable operators affiliated with a von Neumann algebra $\\mathcal{M}$ is necessary inner. If $\\mathcal{M}$ is a properly infinite von Neumann algebra, then every derivation on $LS(\\mathcal{M})$ is inner. In addition, it is proved that any derivation on $\\mathcal{M}$ with values in Banach $\\mathcal{M}$-bimodule of locally measurable operators is inner."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4883","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"}