{"paper":{"title":"C*-algebras generated by multiplication operators and composition operators with rational symbol","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Hiroyasu Hamada","submitted_at":"2015-02-07T03:48:25Z","abstract_excerpt":"Let $R$ be a rational function of degree at least two, let $J_R$ be the Julia set of $R$ and let $\\mu^L$ be the Lyubich measure of $R$. We study the C$^*$-algebra $\\mathcal{MC}_R$ generated by all multiplication operators by continuous functions in $C(J_R)$ and the composition operator $C_R$ induced by $R$ on $L^2(J_R, \\mu^L)$. We show that the C$^*$-algebra $\\mathcal{MC}_R$ is isomorphic to the C$^*$-algebra $\\mathcal{O}_R (J_R)$ associated with the complex dynamical system $\\{R^{\\circ n} \\}_{n=1} ^\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02093","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"}