{"paper":{"title":"Derivations on symmetric quasi-Banach ideals of 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, G. B. Levitina, V. I. Chilin","submitted_at":"2012-04-19T09:36:54Z","abstract_excerpt":"Let $\\mathcal{I,J}$ be symmetric quasi-Banach ideals of compact operators on an infinite-dimensional complex Hilbert space $H$, let $\\mathcal{J:I}$ be a space of multipliers from $\\mathcal{I}$ to $\\mathcal{J}$. Obviously, ideals $\\mathcal{I}$ and $\\mathcal{J}$ are quasi-Banach algebras and it is clear that ideal $\\mathcal{J}$ is a bimodule for $\\mathcal{I}$. We study the set of all derivations from $\\mathcal{I}$ into $\\mathcal{J}$. We show that any such derivation is automatically continuous and there exists an operator $a\\in\\mathcal{J:I}$ such that $\\delta(\\cdot)=[a,\\cdot]$, moreover $\\|a\\|_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4297","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"}