{"paper":{"title":"Bounded cosine functions close to continuous scalar bounded cosine functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jean Esterle (IMB)","submitted_at":"2015-01-31T19:04:29Z","abstract_excerpt":"Let $(C(t))\\_{t \\in R}$ be a cosine function in a unital Banach algebra. We show that if $sup\\_{t\\in R}\\Vert C(t)-cos(t)\\Vert \\textless{} 2$ for some continuous scalar bounded cosine function $(c(t))\\_{t\\in \\R},$ then the closed subalgebra generated by $(C(t))\\_{t\\in R}$ is isomorphic to $\\C^k$ for some positive integer $k.$ If, further, $sup\\_{t\\in \\R}\\Vert C(t)-cos(t)\\Vert \\textless{} {8\\over 3\\sqrt 3},$ or if $c(t)=I$, then $C(t)=c(t)$ for $t\\in R.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00150","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"}