{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6JHLMYCRUZLFCMENUSJ6I5DGJY","short_pith_number":"pith:6JHLMYCR","schema_version":"1.0","canonical_sha256":"f24eb66051a65651308da493e474664e0955aea945e0c85018a556836d3823d0","source":{"kind":"arxiv","id":"1204.4925","version":1},"attestation_state":"computed","paper":{"title":"Determining elements in Banach algebras through spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.OA","authors_text":"M. Bre\\v{s}ar, \\v{S}. \\v{S}penko","submitted_at":"2012-04-22T19:12:58Z","abstract_excerpt":"Let $A$ be a Banach algebra. By $\\sigma(x)$ and $r(x)$ we denote the spectrum and the spectral radius of $x\\in A$, respectively. We consider the relationship between elements $a,b\\in A$ that satisfy one of the following two conditions: (1) $\\sigma(ax) = \\sigma(bx)$ for all $x\\in A$, (2) $r(ax) \\le r(bx)$ for all $x\\in A$. In particular we show that (1) implies $a=b$ if $A$ is a $C^*$-algebra, and (2) implies $a\\in \\mathbb C b$ if $A$ is a prime $C^*$-algebra. As an application of the results concerning the conditions (1) and (2) we obtain some spectral characterizations of multiplicative maps."},"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":"1204.4925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-04-22T19:12:58Z","cross_cats_sorted":["math.FA","math.SP"],"title_canon_sha256":"105757416df8c14788177f36fdbd14a29f1b6f4077a6557e9400e62325fb1bdc","abstract_canon_sha256":"ce99887f731921b5fde0c85152a3b2a989d363b24d32cfa928dc98707060d8f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:15.150037Z","signature_b64":"ZfKw9u+pgBijDZM96sQOiqIUACk2KCp0vLfAuK4+iE7JpiKM2JRgeWceN1i9o50d9mr6Iiv/pYEssZc7AOlYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f24eb66051a65651308da493e474664e0955aea945e0c85018a556836d3823d0","last_reissued_at":"2026-05-18T03:57:15.149634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:15.149634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determining elements in Banach algebras through spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.OA","authors_text":"M. Bre\\v{s}ar, \\v{S}. \\v{S}penko","submitted_at":"2012-04-22T19:12:58Z","abstract_excerpt":"Let $A$ be a Banach algebra. By $\\sigma(x)$ and $r(x)$ we denote the spectrum and the spectral radius of $x\\in A$, respectively. We consider the relationship between elements $a,b\\in A$ that satisfy one of the following two conditions: (1) $\\sigma(ax) = \\sigma(bx)$ for all $x\\in A$, (2) $r(ax) \\le r(bx)$ for all $x\\in A$. In particular we show that (1) implies $a=b$ if $A$ is a $C^*$-algebra, and (2) implies $a\\in \\mathbb C b$ if $A$ is a prime $C^*$-algebra. As an application of the results concerning the conditions (1) and (2) we obtain some spectral characterizations of multiplicative maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4925","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":"1204.4925","created_at":"2026-05-18T03:57:15.149694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.4925v1","created_at":"2026-05-18T03:57:15.149694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4925","created_at":"2026-05-18T03:57:15.149694+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JHLMYCRUZLF","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JHLMYCRUZLFCMEN","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JHLMYCR","created_at":"2026-05-18T12:26:56.085431+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/6JHLMYCRUZLFCMENUSJ6I5DGJY","json":"https://pith.science/pith/6JHLMYCRUZLFCMENUSJ6I5DGJY.json","graph_json":"https://pith.science/api/pith-number/6JHLMYCRUZLFCMENUSJ6I5DGJY/graph.json","events_json":"https://pith.science/api/pith-number/6JHLMYCRUZLFCMENUSJ6I5DGJY/events.json","paper":"https://pith.science/paper/6JHLMYCR"},"agent_actions":{"view_html":"https://pith.science/pith/6JHLMYCRUZLFCMENUSJ6I5DGJY","download_json":"https://pith.science/pith/6JHLMYCRUZLFCMENUSJ6I5DGJY.json","view_paper":"https://pith.science/paper/6JHLMYCR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.4925&json=true","fetch_graph":"https://pith.science/api/pith-number/6JHLMYCRUZLFCMENUSJ6I5DGJY/graph.json","fetch_events":"https://pith.science/api/pith-number/6JHLMYCRUZLFCMENUSJ6I5DGJY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JHLMYCRUZLFCMENUSJ6I5DGJY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JHLMYCRUZLFCMENUSJ6I5DGJY/action/storage_attestation","attest_author":"https://pith.science/pith/6JHLMYCRUZLFCMENUSJ6I5DGJY/action/author_attestation","sign_citation":"https://pith.science/pith/6JHLMYCRUZLFCMENUSJ6I5DGJY/action/citation_signature","submit_replication":"https://pith.science/pith/6JHLMYCRUZLFCMENUSJ6I5DGJY/action/replication_record"}},"created_at":"2026-05-18T03:57:15.149694+00:00","updated_at":"2026-05-18T03:57:15.149694+00:00"}