{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5N77MY27FSRMVZXKTWZYZHELEP","short_pith_number":"pith:5N77MY27","schema_version":"1.0","canonical_sha256":"eb7ff6635f2ca2cae6ea9db38c9c8b23f10575ac9e63d830526d7798362f938d","source":{"kind":"arxiv","id":"1112.0444","version":1},"attestation_state":"computed","paper":{"title":"$^{*}$-Regularity of Operator Space Projective Tensor Product of C$^{*}$-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ajay Kumar, Vandana Rajpal","submitted_at":"2011-12-02T12:25:04Z","abstract_excerpt":"The Banach $^{*}$-algebra $A\\hat{\\otimes}B$, the operator space projective tensor product of $C^{*}$-algebras $A$ and $B$, is shown to be $^{*}$-regular if Tomiyama's property ($F$) holds for $A\\otimes_{\\min}B$ and $A \\otimes_{\\min}B=A \\otimes_{\\max}B$, where $\\otimes_{\\min}$ and $\\otimes_{\\max}$ are the injective and projective $C^{*}$-cross norm, respectively. However, $A\\hat{\\otimes}B$ has a unique $C^{*}$-norm if and only if $A\\otimes B$ has. We also discuss the property ($F$) of $A\\hat{\\otimes}B$ and $A\\otimes_{h}B$, the Haagerup tensor product of $A$ and $B$."},"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":"1112.0444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-12-02T12:25:04Z","cross_cats_sorted":[],"title_canon_sha256":"6495d3e4f2f6a62e6c9cdfb91ee67cba5a837fe0ee7c4f977d9111d29fa5941a","abstract_canon_sha256":"b18a670835859c751d35eb5b3dd03c2636511200a039c1720c92dacf91876879"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:07.200978Z","signature_b64":"WZfOcV7MXtc4ASM1XLT5/gmbYhHE22Cug6bfObWiwvTLQfCkUkcP9LExwQVVyTuqTQMquDh5VElIETm86C9JAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb7ff6635f2ca2cae6ea9db38c9c8b23f10575ac9e63d830526d7798362f938d","last_reissued_at":"2026-05-18T04:07:07.200294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:07.200294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$^{*}$-Regularity of Operator Space Projective Tensor Product of C$^{*}$-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ajay Kumar, Vandana Rajpal","submitted_at":"2011-12-02T12:25:04Z","abstract_excerpt":"The Banach $^{*}$-algebra $A\\hat{\\otimes}B$, the operator space projective tensor product of $C^{*}$-algebras $A$ and $B$, is shown to be $^{*}$-regular if Tomiyama's property ($F$) holds for $A\\otimes_{\\min}B$ and $A \\otimes_{\\min}B=A \\otimes_{\\max}B$, where $\\otimes_{\\min}$ and $\\otimes_{\\max}$ are the injective and projective $C^{*}$-cross norm, respectively. However, $A\\hat{\\otimes}B$ has a unique $C^{*}$-norm if and only if $A\\otimes B$ has. We also discuss the property ($F$) of $A\\hat{\\otimes}B$ and $A\\otimes_{h}B$, the Haagerup tensor product of $A$ and $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0444","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":"1112.0444","created_at":"2026-05-18T04:07:07.200419+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0444v1","created_at":"2026-05-18T04:07:07.200419+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0444","created_at":"2026-05-18T04:07:07.200419+00:00"},{"alias_kind":"pith_short_12","alias_value":"5N77MY27FSRM","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5N77MY27FSRMVZXK","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5N77MY27","created_at":"2026-05-18T12:26:20.644004+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/5N77MY27FSRMVZXKTWZYZHELEP","json":"https://pith.science/pith/5N77MY27FSRMVZXKTWZYZHELEP.json","graph_json":"https://pith.science/api/pith-number/5N77MY27FSRMVZXKTWZYZHELEP/graph.json","events_json":"https://pith.science/api/pith-number/5N77MY27FSRMVZXKTWZYZHELEP/events.json","paper":"https://pith.science/paper/5N77MY27"},"agent_actions":{"view_html":"https://pith.science/pith/5N77MY27FSRMVZXKTWZYZHELEP","download_json":"https://pith.science/pith/5N77MY27FSRMVZXKTWZYZHELEP.json","view_paper":"https://pith.science/paper/5N77MY27","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0444&json=true","fetch_graph":"https://pith.science/api/pith-number/5N77MY27FSRMVZXKTWZYZHELEP/graph.json","fetch_events":"https://pith.science/api/pith-number/5N77MY27FSRMVZXKTWZYZHELEP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5N77MY27FSRMVZXKTWZYZHELEP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5N77MY27FSRMVZXKTWZYZHELEP/action/storage_attestation","attest_author":"https://pith.science/pith/5N77MY27FSRMVZXKTWZYZHELEP/action/author_attestation","sign_citation":"https://pith.science/pith/5N77MY27FSRMVZXKTWZYZHELEP/action/citation_signature","submit_replication":"https://pith.science/pith/5N77MY27FSRMVZXKTWZYZHELEP/action/replication_record"}},"created_at":"2026-05-18T04:07:07.200419+00:00","updated_at":"2026-05-18T04:07:07.200419+00:00"}