{"paper":{"title":"Complex symmetry of Composition operators induced by involutive Ball automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"S.Waleed Noor","submitted_at":"2012-07-03T20:29:10Z","abstract_excerpt":"Suppose $\\mathcal{H}$ is a weighted Hardy space of analytic functions on the unit ball $\\mathbb{B}_n\\subset\\mathbb{C}^n$ such that the composition operator $C_\\psi$ defined by $C_{\\psi}f=f\\circ\\psi$ is bounded on $\\mathcal{H}$ whenever $\\psi$ is a linear fractional self-map of $\\mathbb{B}_n$. If $\\varphi$ is an involutive Moebius automorphism of $\\mathbb{B}_n$, we find a conjugation operator $\\mathcal{J}$ on $\\mathcal{H}$ such that $C_{\\varphi}=\\mathcal{J} C^*_{\\varphi}\\mathcal{J}$. The case $n=1$ answers a question of Garcia and Hammond."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0828","kind":"arxiv","version":2},"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"}