{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZP2COLHVVIO2NHEELBTOGDD6DB","short_pith_number":"pith:ZP2COLHV","schema_version":"1.0","canonical_sha256":"cbf4272cf5aa1da69c845866e30c7e1875d98ad37fd361726c3177f015fdb472","source":{"kind":"arxiv","id":"1404.5819","version":1},"attestation_state":"computed","paper":{"title":"Admissible fundamental operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haripada Sau, Sneh Lata, Tirthankar Bhattacharyya","submitted_at":"2014-04-23T13:32:37Z","abstract_excerpt":"Let $F$ and $G$ be two bounded operators on two Hilbert spaces. Let their numerical radii be no greater than one. This note investigate when there is a $\\Gamma$-contraction $(S,P)$ such that $F$ is the fundamental operator of $(S,P)$ and $G$ is the fundamental operator of $(S^*,P^*)$. Theorem 1 puts a necessary condition on $F$ and $G$ for them to be the fundamental operators of $(S,P)$ and $(S^*,P^*)$ respectively. Theorem 2 shows that this necessary condition is sufficient too provided we restrict our attention to a certain special case. The general case is investigated in Theorem 3. Some of"},"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":"1404.5819","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-23T13:32:37Z","cross_cats_sorted":[],"title_canon_sha256":"7548adee62f365f4afe0a906cb2545f9a91f9c492b04479913a6a5ec884cd365","abstract_canon_sha256":"077c9b3795053add316355dcb41afaee710579912a1cedb0aab3c3695ce87b9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:39.946561Z","signature_b64":"6SL8/98lNZhbYzwoTeDFFQ4SdQqsbNdTM+hG61TdlfqGLzhqpf1KYJPvv7OGvk8Q21YwqM6PjyvLYAFedzMhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbf4272cf5aa1da69c845866e30c7e1875d98ad37fd361726c3177f015fdb472","last_reissued_at":"2026-05-18T00:42:39.946009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:39.946009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Admissible fundamental operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Haripada Sau, Sneh Lata, Tirthankar Bhattacharyya","submitted_at":"2014-04-23T13:32:37Z","abstract_excerpt":"Let $F$ and $G$ be two bounded operators on two Hilbert spaces. Let their numerical radii be no greater than one. This note investigate when there is a $\\Gamma$-contraction $(S,P)$ such that $F$ is the fundamental operator of $(S,P)$ and $G$ is the fundamental operator of $(S^*,P^*)$. Theorem 1 puts a necessary condition on $F$ and $G$ for them to be the fundamental operators of $(S,P)$ and $(S^*,P^*)$ respectively. Theorem 2 shows that this necessary condition is sufficient too provided we restrict our attention to a certain special case. The general case is investigated in Theorem 3. Some of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5819","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":"1404.5819","created_at":"2026-05-18T00:42:39.946087+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5819v1","created_at":"2026-05-18T00:42:39.946087+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5819","created_at":"2026-05-18T00:42:39.946087+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZP2COLHVVIO2","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZP2COLHVVIO2NHEE","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZP2COLHV","created_at":"2026-05-18T12:28:59.999130+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/ZP2COLHVVIO2NHEELBTOGDD6DB","json":"https://pith.science/pith/ZP2COLHVVIO2NHEELBTOGDD6DB.json","graph_json":"https://pith.science/api/pith-number/ZP2COLHVVIO2NHEELBTOGDD6DB/graph.json","events_json":"https://pith.science/api/pith-number/ZP2COLHVVIO2NHEELBTOGDD6DB/events.json","paper":"https://pith.science/paper/ZP2COLHV"},"agent_actions":{"view_html":"https://pith.science/pith/ZP2COLHVVIO2NHEELBTOGDD6DB","download_json":"https://pith.science/pith/ZP2COLHVVIO2NHEELBTOGDD6DB.json","view_paper":"https://pith.science/paper/ZP2COLHV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5819&json=true","fetch_graph":"https://pith.science/api/pith-number/ZP2COLHVVIO2NHEELBTOGDD6DB/graph.json","fetch_events":"https://pith.science/api/pith-number/ZP2COLHVVIO2NHEELBTOGDD6DB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZP2COLHVVIO2NHEELBTOGDD6DB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZP2COLHVVIO2NHEELBTOGDD6DB/action/storage_attestation","attest_author":"https://pith.science/pith/ZP2COLHVVIO2NHEELBTOGDD6DB/action/author_attestation","sign_citation":"https://pith.science/pith/ZP2COLHVVIO2NHEELBTOGDD6DB/action/citation_signature","submit_replication":"https://pith.science/pith/ZP2COLHVVIO2NHEELBTOGDD6DB/action/replication_record"}},"created_at":"2026-05-18T00:42:39.946087+00:00","updated_at":"2026-05-18T00:42:39.946087+00:00"}