{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EVAM3B3WUI5PBPJBW457UONPLY","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":"861475fa8e64d7c1aed20aa0971db5073916025f52de01c81e6118ff977c1e1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-20T23:14:41Z","title_canon_sha256":"cd895e5a45b20cdc7140d4dbfd8cfe58460089bdd9d173a4125447b74cd8fe17"},"schema_version":"1.0","source":{"id":"1112.4878","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4878","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4878v2","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4878","created_at":"2026-05-18T03:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"EVAM3B3WUI5P","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EVAM3B3WUI5PBPJB","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EVAM3B3W","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:57df5d19bc15eb065dbf073e5b331a08d57b1c7828e818bc0b246bc86bf412f0","target":"graph","created_at":"2026-05-18T03:51:23Z","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 study, for a locally compact group $G$, the compactifications $(\\pi,G^\\pi)$ associated with unitary representations $\\pi$, which we call {\\it $\\pi$-Eberlein compactifications}. We also study the Gelfand spectra $\\Phi_{\\mathcal{A}}(\\pi)}$ of the uniformly closed algebras $\\mathcal{A}(\\pi)$ generated by matrix coefficients of such $\\pi$. We note that $\\Phi_{\\mathcal{A}(\\pi)}\\cup\\{0\\}$ is itself a semigroup and show that the \\v{S}ilov boundary of $\\mathcal{A}(\\pi)$ is $G^\\pi$. We study containment relations of various uniformly closed algebras generated by matrix coefficients, and give a new c","authors_text":"Nico Spronk, Ross Stokke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-20T23:14:41Z","title":"Matrix coefficients of unitary representations and associated compactifications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4878","kind":"arxiv","version":2},"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:a9db2ca23a5027ce214b2347f0555df68a6ad681aca1a0a265e5c224b648d450","target":"record","created_at":"2026-05-18T03:51:23Z","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":"861475fa8e64d7c1aed20aa0971db5073916025f52de01c81e6118ff977c1e1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-20T23:14:41Z","title_canon_sha256":"cd895e5a45b20cdc7140d4dbfd8cfe58460089bdd9d173a4125447b74cd8fe17"},"schema_version":"1.0","source":{"id":"1112.4878","kind":"arxiv","version":2}},"canonical_sha256":"2540cd8776a23af0bd21b73bfa39af5e25b8a80a61542e05470d993715ab3ca9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2540cd8776a23af0bd21b73bfa39af5e25b8a80a61542e05470d993715ab3ca9","first_computed_at":"2026-05-18T03:51:23.550598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:23.550598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AiHgeXVwUD/v8wrRRXIiSUBPZLeX1xmiSjIa2pY7a/3KE3R4TdJ9xVjQwCcm0/HXFp9E2FXFZEZMsNCyFhQvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:23.551465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4878","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9db2ca23a5027ce214b2347f0555df68a6ad681aca1a0a265e5c224b648d450","sha256:57df5d19bc15eb065dbf073e5b331a08d57b1c7828e818bc0b246bc86bf412f0"],"state_sha256":"51fdef3460ca3902afe8d8423a009f0813e63726379557e3d15c78b0c0795c46"}