{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OG7FPXTMPE2YUNWWCOMIZIIJSY","short_pith_number":"pith:OG7FPXTM","schema_version":"1.0","canonical_sha256":"71be57de6c79358a36d613988ca109962781254aae4a7f8c19afa8ce4dcf1692","source":{"kind":"arxiv","id":"1509.01922","version":1},"attestation_state":"computed","paper":{"title":"A property for locally convex $^*$-algebras related to Property $(T)$ and character amenability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anthony To-Ming Lau, Chi-Keung Ng, Xiao Chen","submitted_at":"2015-09-07T06:33:08Z","abstract_excerpt":"For a locally convex $^*$-algebra $A$ equipped with a fixed continuous $^*$-character $\\varepsilon$, we define a cohomological property, called property $(FH)$, which is similar to character amenability. Let $C_c(G)$ be the space of continuous functions on a second countable locally compact group $G$ with compact supports, equipped with the convolution $^*$-algebra structure and a certain inductive topology. We show that $(C_c(G), \\varepsilon_G)$ has property $(FH)$ if and only if $G$ has property $(T)$. On the other hand, many Banach algebras equipped with canonical characters have property $"},"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":"1509.01922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-07T06:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"ea14596cc7c5d7c0c77732a243d911ea37aa4978d51561887c0c1d8d182e5363","abstract_canon_sha256":"1b87faec4055a650a08fc0ab3123b1ef2c4cbd1bfed5b7feb537ce40ac497afd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:50.160995Z","signature_b64":"W0Xicp7dGWY0nJC0elBPMA1ON904K+5ZoSNOwDufn1+uTK2itvGaY3tsJOL9D2DAhc7Q1itEOpJleqyewesiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71be57de6c79358a36d613988ca109962781254aae4a7f8c19afa8ce4dcf1692","last_reissued_at":"2026-05-18T01:33:50.160388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:50.160388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A property for locally convex $^*$-algebras related to Property $(T)$ and character amenability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anthony To-Ming Lau, Chi-Keung Ng, Xiao Chen","submitted_at":"2015-09-07T06:33:08Z","abstract_excerpt":"For a locally convex $^*$-algebra $A$ equipped with a fixed continuous $^*$-character $\\varepsilon$, we define a cohomological property, called property $(FH)$, which is similar to character amenability. Let $C_c(G)$ be the space of continuous functions on a second countable locally compact group $G$ with compact supports, equipped with the convolution $^*$-algebra structure and a certain inductive topology. We show that $(C_c(G), \\varepsilon_G)$ has property $(FH)$ if and only if $G$ has property $(T)$. On the other hand, many Banach algebras equipped with canonical characters have property $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01922","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":"1509.01922","created_at":"2026-05-18T01:33:50.160471+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01922v1","created_at":"2026-05-18T01:33:50.160471+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01922","created_at":"2026-05-18T01:33:50.160471+00:00"},{"alias_kind":"pith_short_12","alias_value":"OG7FPXTMPE2Y","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OG7FPXTMPE2YUNWW","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OG7FPXTM","created_at":"2026-05-18T12:29:34.919912+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/OG7FPXTMPE2YUNWWCOMIZIIJSY","json":"https://pith.science/pith/OG7FPXTMPE2YUNWWCOMIZIIJSY.json","graph_json":"https://pith.science/api/pith-number/OG7FPXTMPE2YUNWWCOMIZIIJSY/graph.json","events_json":"https://pith.science/api/pith-number/OG7FPXTMPE2YUNWWCOMIZIIJSY/events.json","paper":"https://pith.science/paper/OG7FPXTM"},"agent_actions":{"view_html":"https://pith.science/pith/OG7FPXTMPE2YUNWWCOMIZIIJSY","download_json":"https://pith.science/pith/OG7FPXTMPE2YUNWWCOMIZIIJSY.json","view_paper":"https://pith.science/paper/OG7FPXTM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01922&json=true","fetch_graph":"https://pith.science/api/pith-number/OG7FPXTMPE2YUNWWCOMIZIIJSY/graph.json","fetch_events":"https://pith.science/api/pith-number/OG7FPXTMPE2YUNWWCOMIZIIJSY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OG7FPXTMPE2YUNWWCOMIZIIJSY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OG7FPXTMPE2YUNWWCOMIZIIJSY/action/storage_attestation","attest_author":"https://pith.science/pith/OG7FPXTMPE2YUNWWCOMIZIIJSY/action/author_attestation","sign_citation":"https://pith.science/pith/OG7FPXTMPE2YUNWWCOMIZIIJSY/action/citation_signature","submit_replication":"https://pith.science/pith/OG7FPXTMPE2YUNWWCOMIZIIJSY/action/replication_record"}},"created_at":"2026-05-18T01:33:50.160471+00:00","updated_at":"2026-05-18T01:33:50.160471+00:00"}