{"paper":{"title":"Stability of derivations under weak-2-local continuous perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Enrique Jord\\'a","submitted_at":"2016-05-18T16:56:17Z","abstract_excerpt":"Let $\\Omega$ be a compact Hausdorff space and let $A$ be a C$^*$-algebra. We prove that if every weak-2-local derivation on $A$ is a linear derivation and every derivation on $C(\\Omega,A)$ is inner, then every weak-2-local derivation $\\Delta:C(\\Omega,A)\\to C(\\Omega,A)$ is a {\\rm(}linear{\\rm)} derivation. As a consequence we derive that, for every complex Hilbert space $H$, every weak-2-local derivation $\\Delta : C(\\Omega,B(H)) \\to C(\\Omega,B(H))$ is a (linear) derivation. We actually show that the same conclusion remains true when $B(H)$ is replaced with an atomic von Neumann algebra. With a m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05656","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"}