{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:KFKLQTAJMFGHDMYDMLBSTMTY7A","short_pith_number":"pith:KFKLQTAJ","schema_version":"1.0","canonical_sha256":"5154b84c09614c71b30362c329b278f81d063af793e084ae6f91e14bbc584305","source":{"kind":"arxiv","id":"1011.3797","version":2},"attestation_state":"computed","paper":{"title":"Operator algebras with contractive approximate identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.OA","authors_text":"Charles John Read, David P. Blecher","submitted_at":"2010-11-16T19:42:29Z","abstract_excerpt":"We give several applications of a recent theorem of the second author, which solved a conjecture of the first author with Hay and Neal, concerning contractive approximate identities; and another of Hay from the theory of noncommutative peak sets, thereby putting the latter theory on a much firmer foundation. From this theorem it emerges there is a surprising amount of positivity present in any operator algebras with contractive approximate identity. We exploit this to generalize several results previously available only for $C^*$-algebras, and we give many other applications."},"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":"1011.3797","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-11-16T19:42:29Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"7dfda2ef601d6797984ffedf57ceaaeb642bfafe5a12b87a1b233916f04d4a5d","abstract_canon_sha256":"92dee8f309d67a25a96fa6359037fa8e0a95f541d86019c9d422778b4644529c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:19.880843Z","signature_b64":"Kmes6+kAPVSNmK8tTdQqGWhxDgxQOtMs+IWBykBysoYy2vdccXafqbID/NAYr2L7+FL7Pr6/gQXWwqZUSPdmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5154b84c09614c71b30362c329b278f81d063af793e084ae6f91e14bbc584305","last_reissued_at":"2026-05-18T04:28:19.880357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:19.880357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operator algebras with contractive approximate identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.OA","authors_text":"Charles John Read, David P. Blecher","submitted_at":"2010-11-16T19:42:29Z","abstract_excerpt":"We give several applications of a recent theorem of the second author, which solved a conjecture of the first author with Hay and Neal, concerning contractive approximate identities; and another of Hay from the theory of noncommutative peak sets, thereby putting the latter theory on a much firmer foundation. From this theorem it emerges there is a surprising amount of positivity present in any operator algebras with contractive approximate identity. We exploit this to generalize several results previously available only for $C^*$-algebras, and we give many other applications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3797","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":"1011.3797","created_at":"2026-05-18T04:28:19.880443+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3797v2","created_at":"2026-05-18T04:28:19.880443+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3797","created_at":"2026-05-18T04:28:19.880443+00:00"},{"alias_kind":"pith_short_12","alias_value":"KFKLQTAJMFGH","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"KFKLQTAJMFGHDMYD","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"KFKLQTAJ","created_at":"2026-05-18T12:26:09.077623+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/KFKLQTAJMFGHDMYDMLBSTMTY7A","json":"https://pith.science/pith/KFKLQTAJMFGHDMYDMLBSTMTY7A.json","graph_json":"https://pith.science/api/pith-number/KFKLQTAJMFGHDMYDMLBSTMTY7A/graph.json","events_json":"https://pith.science/api/pith-number/KFKLQTAJMFGHDMYDMLBSTMTY7A/events.json","paper":"https://pith.science/paper/KFKLQTAJ"},"agent_actions":{"view_html":"https://pith.science/pith/KFKLQTAJMFGHDMYDMLBSTMTY7A","download_json":"https://pith.science/pith/KFKLQTAJMFGHDMYDMLBSTMTY7A.json","view_paper":"https://pith.science/paper/KFKLQTAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3797&json=true","fetch_graph":"https://pith.science/api/pith-number/KFKLQTAJMFGHDMYDMLBSTMTY7A/graph.json","fetch_events":"https://pith.science/api/pith-number/KFKLQTAJMFGHDMYDMLBSTMTY7A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KFKLQTAJMFGHDMYDMLBSTMTY7A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KFKLQTAJMFGHDMYDMLBSTMTY7A/action/storage_attestation","attest_author":"https://pith.science/pith/KFKLQTAJMFGHDMYDMLBSTMTY7A/action/author_attestation","sign_citation":"https://pith.science/pith/KFKLQTAJMFGHDMYDMLBSTMTY7A/action/citation_signature","submit_replication":"https://pith.science/pith/KFKLQTAJMFGHDMYDMLBSTMTY7A/action/replication_record"}},"created_at":"2026-05-18T04:28:19.880443+00:00","updated_at":"2026-05-18T04:28:19.880443+00:00"}