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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.08632","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-29T08:21:15Z","cross_cats_sorted":[],"title_canon_sha256":"9afeef4c37331491feda42b045cfef4c9679149f20c983ed8d517a13fe934217","abstract_canon_sha256":"ba4b9ace614812afeafd46669d7582d593bc6abcd370121e13df4d1d896e7a80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:00.893377Z","signature_b64":"9XkRq/p5oKspdWy1x7PJpxzJ78zypxicFERygWVyL9/03oOuWdR0Rdx60V8j6u7PhdikJalpRGkEEjFhbMRkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e804b0be440f1aa947ef4d885531b55de11c9735127598963cbe0da6c90ae6d2","last_reissued_at":"2026-05-18T01:21:00.892928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:00.892928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.08632","created_at":"2026-05-18T01:21:00.892998+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.08632v2","created_at":"2026-05-18T01:21:00.892998+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08632","created_at":"2026-05-18T01:21:00.892998+00:00"},{"alias_kind":"pith_short_12","alias_value":"5ACLBPSEB4NK","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5ACLBPSEB4NKSR7P","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5ACLBPSE","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX","json":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX.json","graph_json":"https://pith.science/api/pith-number/5ACLBPSEB4NKSR7PJWEFKMNVLX/graph.json","events_json":"https://pith.science/api/pith-number/5ACLBPSEB4NKSR7PJWEFKMNVLX/events.json","paper":"https://pith.science/paper/5ACLBPSE"},"agent_actions":{"view_html":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX","download_json":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX.json","view_paper":"https://pith.science/paper/5ACLBPSE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.08632&json=true","fetch_graph":"https://pith.science/api/pith-number/5ACLBPSEB4NKSR7PJWEFKMNVLX/graph.json","fetch_events":"https://pith.science/api/pith-number/5ACLBPSEB4NKSR7PJWEFKMNVLX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX/action/storage_attestation","attest_author":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX/action/author_attestation","sign_citation":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX/action/citation_signature","submit_replication":"https://pith.science/pith/5ACLBPSEB4NKSR7PJWEFKMNVLX/action/replication_record"}},"created_at":"2026-05-18T01:21:00.892998+00:00","updated_at":"2026-05-18T01:21:00.892998+00:00"}