{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4RBLENACM6V2UFJQSOMPEEKBA2","short_pith_number":"pith:4RBLENAC","schema_version":"1.0","canonical_sha256":"e442b2340267abaa15309398f21141068132486637a94e93173fe28cb16a2396","source":{"kind":"arxiv","id":"1811.05174","version":1},"attestation_state":"computed","paper":{"title":"Composition operators with surjective symbol and small approximation numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Li (LML), Herv\\'e Queff\\'elec (LPP), Luis Rodr\\'iguez-Piazza","submitted_at":"2018-11-13T09:17:32Z","abstract_excerpt":"We give a new proof of the existence of a surjective symbol whose associated composition operator on H 2 (D) is in all Schatten classes, with the improvement that its approximation numbers can be, in some sense, arbitrarily small. We show, as an application, that, contrary to the 1-dimensional case, for N $\\ge$ 2, the behavior of the approximation numbers a n = a n (C $\\Phi$), or rather of $\\beta$ -- N = lim inf n$\\rightarrow$$\\infty$ [a n ] 1/n 1/N or $\\beta$ + N = lim sup n$\\rightarrow$$\\infty$ [a n ] 1/n 1/N , of composition operators on H 2 (D N) cannot be determined by the image of the sy"},"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":"1811.05174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-13T09:17:32Z","cross_cats_sorted":[],"title_canon_sha256":"f1ff0b778cc8cb65172334a7fccaa50a658f3044f09380f1934922e0c9a72ec2","abstract_canon_sha256":"a479a386e8f443bf4a473d868372386e9a8218c97543c5a8b4217dfbb52b3cf5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:46.701156Z","signature_b64":"acjX15LguoMKdSyTofqyAW2wOjgM0oD8c7YADiNP9Qf710FqBIomBvFAdBSnTuy/sWSJ+e2DVXiyqiHGrTS/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e442b2340267abaa15309398f21141068132486637a94e93173fe28cb16a2396","last_reissued_at":"2026-05-18T00:00:46.700727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:46.700727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Composition operators with surjective symbol and small approximation numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Li (LML), Herv\\'e Queff\\'elec (LPP), Luis Rodr\\'iguez-Piazza","submitted_at":"2018-11-13T09:17:32Z","abstract_excerpt":"We give a new proof of the existence of a surjective symbol whose associated composition operator on H 2 (D) is in all Schatten classes, with the improvement that its approximation numbers can be, in some sense, arbitrarily small. We show, as an application, that, contrary to the 1-dimensional case, for N $\\ge$ 2, the behavior of the approximation numbers a n = a n (C $\\Phi$), or rather of $\\beta$ -- N = lim inf n$\\rightarrow$$\\infty$ [a n ] 1/n 1/N or $\\beta$ + N = lim sup n$\\rightarrow$$\\infty$ [a n ] 1/n 1/N , of composition operators on H 2 (D N) cannot be determined by the image of the sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05174","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.05174","created_at":"2026-05-18T00:00:46.700791+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.05174v1","created_at":"2026-05-18T00:00:46.700791+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.05174","created_at":"2026-05-18T00:00:46.700791+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RBLENACM6V2","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RBLENACM6V2UFJQ","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RBLENAC","created_at":"2026-05-18T12:32:05.422762+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/4RBLENACM6V2UFJQSOMPEEKBA2","json":"https://pith.science/pith/4RBLENACM6V2UFJQSOMPEEKBA2.json","graph_json":"https://pith.science/api/pith-number/4RBLENACM6V2UFJQSOMPEEKBA2/graph.json","events_json":"https://pith.science/api/pith-number/4RBLENACM6V2UFJQSOMPEEKBA2/events.json","paper":"https://pith.science/paper/4RBLENAC"},"agent_actions":{"view_html":"https://pith.science/pith/4RBLENACM6V2UFJQSOMPEEKBA2","download_json":"https://pith.science/pith/4RBLENACM6V2UFJQSOMPEEKBA2.json","view_paper":"https://pith.science/paper/4RBLENAC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.05174&json=true","fetch_graph":"https://pith.science/api/pith-number/4RBLENACM6V2UFJQSOMPEEKBA2/graph.json","fetch_events":"https://pith.science/api/pith-number/4RBLENACM6V2UFJQSOMPEEKBA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RBLENACM6V2UFJQSOMPEEKBA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RBLENACM6V2UFJQSOMPEEKBA2/action/storage_attestation","attest_author":"https://pith.science/pith/4RBLENACM6V2UFJQSOMPEEKBA2/action/author_attestation","sign_citation":"https://pith.science/pith/4RBLENACM6V2UFJQSOMPEEKBA2/action/citation_signature","submit_replication":"https://pith.science/pith/4RBLENACM6V2UFJQSOMPEEKBA2/action/replication_record"}},"created_at":"2026-05-18T00:00:46.700791+00:00","updated_at":"2026-05-18T00:00:46.700791+00:00"}