{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UAPJ5YGHS6M4OAGS5TATSMDFAE","short_pith_number":"pith:UAPJ5YGH","schema_version":"1.0","canonical_sha256":"a01e9ee0c79799c700d2ecc1393065011f80e75b3e9b8cdc661f6da83cf48013","source":{"kind":"arxiv","id":"1601.02941","version":1},"attestation_state":"computed","paper":{"title":"Closed subspaces and some basic topological properties of noncommutative Orlicz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Lining Jiang, Zhenhua Ma","submitted_at":"2016-01-06T11:31:40Z","abstract_excerpt":"In this paper, we study the noncommutative Orlicz space $L_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)$, which generalizes the concept of noncommutative $L^{p}$ space, where $\\mathcal{M}$ is a von Neumann algebra, and $\\varphi$ is an Orlicz function. As a modular space, the space $L_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)$ possesses the Fatou property, and consequently, it is a Banach space. In addition, a new description of the subspace $E_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)=\\overline{\\mathcal{M}\\bigcap L_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)}$ in $L_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)$"},"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":"1601.02941","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-01-06T11:31:40Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"4de323ed36f14d8898cd6436722183452a300f9bebf59be3deee474f34e8becb","abstract_canon_sha256":"4a47b613dce72560c741b042a64efdc0b492becc8a367ba95c5073e9fadf41ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:59.288577Z","signature_b64":"ds7L8zSwUxvjXufJYcbUd56lz6K+5DZfHtZy6uUViC3cknPnzrRhAR1Nyl9uwQQP6lSnJogYV+IX4sGm9k/5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a01e9ee0c79799c700d2ecc1393065011f80e75b3e9b8cdc661f6da83cf48013","last_reissued_at":"2026-05-18T01:22:59.288016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:59.288016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed subspaces and some basic topological properties of noncommutative Orlicz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Lining Jiang, Zhenhua Ma","submitted_at":"2016-01-06T11:31:40Z","abstract_excerpt":"In this paper, we study the noncommutative Orlicz space $L_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)$, which generalizes the concept of noncommutative $L^{p}$ space, where $\\mathcal{M}$ is a von Neumann algebra, and $\\varphi$ is an Orlicz function. As a modular space, the space $L_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)$ possesses the Fatou property, and consequently, it is a Banach space. In addition, a new description of the subspace $E_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)=\\overline{\\mathcal{M}\\bigcap L_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)}$ in $L_{\\varphi}(\\widetilde{\\mathcal{M}},\\tau)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02941","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":"1601.02941","created_at":"2026-05-18T01:22:59.288094+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.02941v1","created_at":"2026-05-18T01:22:59.288094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02941","created_at":"2026-05-18T01:22:59.288094+00:00"},{"alias_kind":"pith_short_12","alias_value":"UAPJ5YGHS6M4","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UAPJ5YGHS6M4OAGS","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UAPJ5YGH","created_at":"2026-05-18T12:30:46.583412+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/UAPJ5YGHS6M4OAGS5TATSMDFAE","json":"https://pith.science/pith/UAPJ5YGHS6M4OAGS5TATSMDFAE.json","graph_json":"https://pith.science/api/pith-number/UAPJ5YGHS6M4OAGS5TATSMDFAE/graph.json","events_json":"https://pith.science/api/pith-number/UAPJ5YGHS6M4OAGS5TATSMDFAE/events.json","paper":"https://pith.science/paper/UAPJ5YGH"},"agent_actions":{"view_html":"https://pith.science/pith/UAPJ5YGHS6M4OAGS5TATSMDFAE","download_json":"https://pith.science/pith/UAPJ5YGHS6M4OAGS5TATSMDFAE.json","view_paper":"https://pith.science/paper/UAPJ5YGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.02941&json=true","fetch_graph":"https://pith.science/api/pith-number/UAPJ5YGHS6M4OAGS5TATSMDFAE/graph.json","fetch_events":"https://pith.science/api/pith-number/UAPJ5YGHS6M4OAGS5TATSMDFAE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UAPJ5YGHS6M4OAGS5TATSMDFAE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UAPJ5YGHS6M4OAGS5TATSMDFAE/action/storage_attestation","attest_author":"https://pith.science/pith/UAPJ5YGHS6M4OAGS5TATSMDFAE/action/author_attestation","sign_citation":"https://pith.science/pith/UAPJ5YGHS6M4OAGS5TATSMDFAE/action/citation_signature","submit_replication":"https://pith.science/pith/UAPJ5YGHS6M4OAGS5TATSMDFAE/action/replication_record"}},"created_at":"2026-05-18T01:22:59.288094+00:00","updated_at":"2026-05-18T01:22:59.288094+00:00"}