{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YZHYNI4SZ5NQOIPS5MCSCGS2IH","short_pith_number":"pith:YZHYNI4S","schema_version":"1.0","canonical_sha256":"c64f86a392cf5b0721f2eb05211a5a41d40eef0572aeb35c528916ab19c16c4d","source":{"kind":"arxiv","id":"1209.6323","version":1},"attestation_state":"computed","paper":{"title":"Subideals of operators II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"G. Weiss, S. Patnaik","submitted_at":"2012-09-27T18:28:48Z","abstract_excerpt":"A subideal (also called a J-ideal) is an ideal of a B(H)-ideal J. This paper is the sequel to Subideals of operators where a complete characterization of principal and then finitely generated J-ideals were obtained by first generalizing the 1983 work of Fong and Radjavi who determined which principal K(H)-ideals are also B(H)-ideals. Here we determine which countably generated J-ideals are B(H)-ideals, and in the absence of the continuum hypothesis which J-ideals with generating sets of cardinality less than the continuum are B(H)-ideals. These and some other results herein are based on the di"},"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":"1209.6323","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-27T18:28:48Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"179031eb498edca7f0a15c614bd16379e6fc63815fb9a9a9d073b70dbdeda9d4","abstract_canon_sha256":"29baab3873aead52d6ca108555b0352a316182c90275e57e334ffa59aff87a5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:34.595810Z","signature_b64":"xL3uwSW12ECI0PjvaikvQEN96ar+uOojNYGQ6p4umuni96UR60lfkbKZ6/cpxKWKMYaPSVXDRFX+cQqdwpElDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c64f86a392cf5b0721f2eb05211a5a41d40eef0572aeb35c528916ab19c16c4d","last_reissued_at":"2026-05-18T03:44:34.595054Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:34.595054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subideals of operators II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"G. Weiss, S. Patnaik","submitted_at":"2012-09-27T18:28:48Z","abstract_excerpt":"A subideal (also called a J-ideal) is an ideal of a B(H)-ideal J. This paper is the sequel to Subideals of operators where a complete characterization of principal and then finitely generated J-ideals were obtained by first generalizing the 1983 work of Fong and Radjavi who determined which principal K(H)-ideals are also B(H)-ideals. Here we determine which countably generated J-ideals are B(H)-ideals, and in the absence of the continuum hypothesis which J-ideals with generating sets of cardinality less than the continuum are B(H)-ideals. These and some other results herein are based on the di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6323","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":"1209.6323","created_at":"2026-05-18T03:44:34.595161+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.6323v1","created_at":"2026-05-18T03:44:34.595161+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6323","created_at":"2026-05-18T03:44:34.595161+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZHYNI4SZ5NQ","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZHYNI4SZ5NQOIPS","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZHYNI4S","created_at":"2026-05-18T12:27:30.460161+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/YZHYNI4SZ5NQOIPS5MCSCGS2IH","json":"https://pith.science/pith/YZHYNI4SZ5NQOIPS5MCSCGS2IH.json","graph_json":"https://pith.science/api/pith-number/YZHYNI4SZ5NQOIPS5MCSCGS2IH/graph.json","events_json":"https://pith.science/api/pith-number/YZHYNI4SZ5NQOIPS5MCSCGS2IH/events.json","paper":"https://pith.science/paper/YZHYNI4S"},"agent_actions":{"view_html":"https://pith.science/pith/YZHYNI4SZ5NQOIPS5MCSCGS2IH","download_json":"https://pith.science/pith/YZHYNI4SZ5NQOIPS5MCSCGS2IH.json","view_paper":"https://pith.science/paper/YZHYNI4S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.6323&json=true","fetch_graph":"https://pith.science/api/pith-number/YZHYNI4SZ5NQOIPS5MCSCGS2IH/graph.json","fetch_events":"https://pith.science/api/pith-number/YZHYNI4SZ5NQOIPS5MCSCGS2IH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZHYNI4SZ5NQOIPS5MCSCGS2IH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZHYNI4SZ5NQOIPS5MCSCGS2IH/action/storage_attestation","attest_author":"https://pith.science/pith/YZHYNI4SZ5NQOIPS5MCSCGS2IH/action/author_attestation","sign_citation":"https://pith.science/pith/YZHYNI4SZ5NQOIPS5MCSCGS2IH/action/citation_signature","submit_replication":"https://pith.science/pith/YZHYNI4SZ5NQOIPS5MCSCGS2IH/action/replication_record"}},"created_at":"2026-05-18T03:44:34.595161+00:00","updated_at":"2026-05-18T03:44:34.595161+00:00"}