{"paper":{"title":"Normal, cohyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mahmood Haji Shaabani, Mahsa Fatehi","submitted_at":"2015-09-29T08:21:15Z","abstract_excerpt":"If $\\psi$ is analytic on the open unit disk $\\mathbb{D}$ and $\\varphi$ is an analytic self-map of $\\mathbb{D}$, the weighted composition operator $C_{\\psi,\\varphi}$ is defined by $C_{\\psi,\\varphi}f(z)=\\psi(z)f (\\varphi (z))$, when $f$ is analytic on $\\mathbb{D}$. In this paper, we study normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces $H^{2}(\\beta)$, we prove that if $C_{\\psi,\\varphi}$ is cohyponormal on $H^{2}(\\beta)$, then $\\psi$ never vanishes on $\\mathbb{D}$ and $\\varphi$ is univale"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08632","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"}