{"paper":{"title":"Composition Operators and Endomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Dennis Courtney, Paul S. Muhly, Samuel W. Schmidt","submitted_at":"2010-03-14T19:30:51Z","abstract_excerpt":"If $b$ is an inner function, then composition with $b$ induces an endomorphism, $\\beta$, of $L^\\infty(\\mathbb{T})$ that leaves $H^\\infty(\\mathbb{T})$ invariant. We investigate the structure of the endomorphisms of $B(L^2(\\mathbb{T}))$  and $B(H^2(\\mathbb{T}))$ that implement $\\beta$ through the representations of $L^\\infty(\\mathbb{T})$ and $H^\\infty(\\mathbb{T})$ in terms of multiplication operators on  $L^2(\\mathbb{T})$  and $H^2(\\mathbb{T})$. Our analysis, which is based on work of R. Rochberg and J. McDonald, will wind its way through the theory of composition operators on spaces of analytic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2806","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"}