{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NBGL6PFAJA5VFO2FNNWH7MTNVI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8de617c07f91291b44819387e39f50726a561e0dafb400f8a02434398e60b85a","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-07T13:36:35Z","title_canon_sha256":"d1fd84fd880c7098f873f66b0423c5dd9ee530feb16d303828f7762802037237"},"schema_version":"1.0","source":{"id":"1705.02623","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02623","created_at":"2026-05-18T00:35:16Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02623v1","created_at":"2026-05-18T00:35:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02623","created_at":"2026-05-18T00:35:16Z"},{"alias_kind":"pith_short_12","alias_value":"NBGL6PFAJA5V","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NBGL6PFAJA5VFO2F","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NBGL6PFA","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:c82215a2e48191982119a5cac87cfaef63df292ec48fb4baf64bd6c8c2e249ee","target":"graph","created_at":"2026-05-18T00:35:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that the crossed product Banach algebra $\\ell^1(G,A;\\alpha)$ that is associated with a ${\\mathrm C}^\\ast$-dynamical system $(A,G,\\alpha)$ is amenable if $G$ is a discrete amenable group and $A$ is a strongly amenable ${\\mathrm C}^\\ast$-algebra. This is a consequence of the combination of a more general result with Paterson's characterisation of strongly amenable unital $\\mathrm{C}^\\ast$-algebras in terms of invariant means for their unitary groups.","authors_text":"Marcel de Jeu, Paulo R. Pinto, Rachid El Harti","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-07T13:36:35Z","title":"Amenable crossed product Banach algebras associated with a class of $\\mathrm{C}^\\ast$-dynamical systems. II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02623","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d62d34e9b70852942c0976f3113d176b7ae7ee1ef4855e10782267df40029305","target":"record","created_at":"2026-05-18T00:35:16Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8de617c07f91291b44819387e39f50726a561e0dafb400f8a02434398e60b85a","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-07T13:36:35Z","title_canon_sha256":"d1fd84fd880c7098f873f66b0423c5dd9ee530feb16d303828f7762802037237"},"schema_version":"1.0","source":{"id":"1705.02623","kind":"arxiv","version":1}},"canonical_sha256":"684cbf3ca0483b52bb456b6c7fb26daa1df36b4f8f16d9b1c805919feb772468","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"684cbf3ca0483b52bb456b6c7fb26daa1df36b4f8f16d9b1c805919feb772468","first_computed_at":"2026-05-18T00:35:16.228010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:16.228010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EWEviHlt2U41Q12z0RoLlMB0whvkW0z/Cl6j5J6NbqvqTcki9uAP1zMQS8eTpLekQkL20xTrWAqkXMwEocMuBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:16.228587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02623","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d62d34e9b70852942c0976f3113d176b7ae7ee1ef4855e10782267df40029305","sha256:c82215a2e48191982119a5cac87cfaef63df292ec48fb4baf64bd6c8c2e249ee"],"state_sha256":"4cc1b2b1732ff3bdd1858e1b0fe06880e155c89c2bf9f2268c2109d87438a63d"}