{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LW4TJXAYVRC4HC7OKCSDDGC4QT","short_pith_number":"pith:LW4TJXAY","schema_version":"1.0","canonical_sha256":"5db934dc18ac45c38bee50a431985c84d7c1546cc8721cddcba64d1d6435e393","source":{"kind":"arxiv","id":"1712.05920","version":1},"attestation_state":"computed","paper":{"title":"On character space of the algebra of BSE-functions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Fozouni","submitted_at":"2017-12-16T08:42:35Z","abstract_excerpt":"Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{\\rm{BSE}}(\\Delta(A))$ consisting of all BSE-functions on $\\Delta(A)$ where $\\Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterization of $\\Delta(C_{\\rm{BSE}}(\\Delta(A)))$ and in the general case we give a partial answer. Also, using the Fourier algebra, we show that $C_{\\rm{BSE}}(\\Delta(A))$ is not a $C^*$-algebra in general. Fina"},"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":"1712.05920","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.FA","submitted_at":"2017-12-16T08:42:35Z","cross_cats_sorted":[],"title_canon_sha256":"faed2abeda06a066573babfa15964b684c4a589d7c6cea66e91d207791965e24","abstract_canon_sha256":"bf6073016f8d4082d71147c921136248e865cc6cf54defaa26a9d055163cf6f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:51.486896Z","signature_b64":"IpK8hpzgWf8tdQOpYaTS6BDjXt7Nilh/afQYwnXaBEcIIoduVEs0YuMjwt6CleSXEcafhR+EDuf+fTgzy0V5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5db934dc18ac45c38bee50a431985c84d7c1546cc8721cddcba64d1d6435e393","last_reissued_at":"2026-05-18T00:27:51.486223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:51.486223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On character space of the algebra of BSE-functions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mohammad Fozouni","submitted_at":"2017-12-16T08:42:35Z","abstract_excerpt":"Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{\\rm{BSE}}(\\Delta(A))$ consisting of all BSE-functions on $\\Delta(A)$ where $\\Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterization of $\\Delta(C_{\\rm{BSE}}(\\Delta(A)))$ and in the general case we give a partial answer. Also, using the Fourier algebra, we show that $C_{\\rm{BSE}}(\\Delta(A))$ is not a $C^*$-algebra in general. Fina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05920","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":"1712.05920","created_at":"2026-05-18T00:27:51.486332+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.05920v1","created_at":"2026-05-18T00:27:51.486332+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05920","created_at":"2026-05-18T00:27:51.486332+00:00"},{"alias_kind":"pith_short_12","alias_value":"LW4TJXAYVRC4","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LW4TJXAYVRC4HC7O","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LW4TJXAY","created_at":"2026-05-18T12:31:28.150371+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/LW4TJXAYVRC4HC7OKCSDDGC4QT","json":"https://pith.science/pith/LW4TJXAYVRC4HC7OKCSDDGC4QT.json","graph_json":"https://pith.science/api/pith-number/LW4TJXAYVRC4HC7OKCSDDGC4QT/graph.json","events_json":"https://pith.science/api/pith-number/LW4TJXAYVRC4HC7OKCSDDGC4QT/events.json","paper":"https://pith.science/paper/LW4TJXAY"},"agent_actions":{"view_html":"https://pith.science/pith/LW4TJXAYVRC4HC7OKCSDDGC4QT","download_json":"https://pith.science/pith/LW4TJXAYVRC4HC7OKCSDDGC4QT.json","view_paper":"https://pith.science/paper/LW4TJXAY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.05920&json=true","fetch_graph":"https://pith.science/api/pith-number/LW4TJXAYVRC4HC7OKCSDDGC4QT/graph.json","fetch_events":"https://pith.science/api/pith-number/LW4TJXAYVRC4HC7OKCSDDGC4QT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LW4TJXAYVRC4HC7OKCSDDGC4QT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LW4TJXAYVRC4HC7OKCSDDGC4QT/action/storage_attestation","attest_author":"https://pith.science/pith/LW4TJXAYVRC4HC7OKCSDDGC4QT/action/author_attestation","sign_citation":"https://pith.science/pith/LW4TJXAYVRC4HC7OKCSDDGC4QT/action/citation_signature","submit_replication":"https://pith.science/pith/LW4TJXAYVRC4HC7OKCSDDGC4QT/action/replication_record"}},"created_at":"2026-05-18T00:27:51.486332+00:00","updated_at":"2026-05-18T00:27:51.486332+00:00"}