{"paper":{"title":"Local derivations on subalgebras of $\\tau$-measurable operators with respect to semi-finite von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Farrukh Mukhamedov, Karimbergen Kudaybergenov","submitted_at":"2014-10-07T05:25:39Z","abstract_excerpt":"This paper is devoted to local derivations on subalgebras on the algebra $S(M, \\tau)$ of all $\\tau$-measurable operators affiliated with a von Neumann algebra $M$ without abelian summands and with a faithful normal semi-finite trace $\\tau.$ We prove that if $\\mathcal{A}$ is a solid $\\ast$-subalgebra in $S(M, \\tau)$ such that $p\\in \\mathcal{A}$ for all projection $p\\in M$ with finite trace, then every local derivation on the algebra $\\mathcal{A}$ is a derivation. This result is new even in the case standard subalgebras on the algebra $B(H)$ of all bounded linear operators on a Hilbert space $H."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1619","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"}