{"paper":{"title":"Derivations on ideals in commutative $AW^*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"G. B. Levitina, V. I. Chilin","submitted_at":"2012-05-28T11:38:48Z","abstract_excerpt":"Let $\\mathcal{A}$ be a commutative $AW^*$-algebra, let $S(\\mathcal{A})$ be the *-algebra of all measurable operators affiliated with $\\mathcal{A}$, let $\\mathcal{I}$ be an ideal in $\\mathcal{A}$, let $s(\\mathcal{I})$ be the support of the ideal $\\mathcal{I}$ and let $\\mathbb{Y}$ be a solid subspace in $S(\\mathcal{A})$. The necessary and sufficient conditions of existence of non-zero band preserving derivations from $\\mathcal{I}$ to $\\mathbb{Y}$ are given. We show that, in case when $\\mathbb{Y}\\subset\\mathcal{A}$, or $\\mathbb{Y}$ is a quasi-normed solid space, any band preserving derivation fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6083","kind":"arxiv","version":3},"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"}