{"paper":{"title":"Derivations in the Banach ideals of $\\tau$-compact 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","submitted_at":"2012-04-18T11:35:04Z","abstract_excerpt":"Let $\\mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semi-finite trace $\\tau$ and let $S_0(\\tau)$ be the algebra of all $\\tau$-compact operators affiliated with $\\mathcal{M}$. Let $E(\\tau)\\subseteq S_0(\\tau)$ be a symmetric operator space (on $\\mathcal{M}$) and let $\\mathcal{E}$ be a symmetrically-normed Banach ideal of $\\tau$-compact operators in $\\mathcal{M}$. We study (i) derivations $\\delta$ on $\\mathcal{M}$ with the range in $E(\\tau)$ and (ii) derivations on the Banach algebra $\\mathcal{E}$. In the first case our main results assert that such derivations are continuo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4052","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"}