{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OOLYBY75AEU77TF6EW25NU6FDY","short_pith_number":"pith:OOLYBY75","schema_version":"1.0","canonical_sha256":"739780e3fd0129ffccbe25b5d6d3c51e1cea510262adfa68bff83a2eec2b04c5","source":{"kind":"arxiv","id":"1204.4942","version":1},"attestation_state":"computed","paper":{"title":"Identifying derivations through the spectra of their values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.OA","authors_text":"B. Magajna, M. Bre\\v{s}ar, \\v{S}. \\v{S}penko","submitted_at":"2012-04-22T21:43:43Z","abstract_excerpt":"We consider the relationship between derivations $d$ and $g$ of a Banach algebra $B$ that satisfy $\\s(g(x)) \\subseteq \\s(d(x))$ for every $x\\in B$, where $\\s(\\, . \\,)$ stands for the spectrum. It turns out that in some basic situations, say if $B=B(X)$, the only possibilities are that $g=d$, $g=0$, and, if $d$ is an inner derivation implemented by an algebraic element of degree 2, also $g=-d$. The conclusions in more complex classes of algebras are not so simple, but are of a similar spirit. A rather definitive result is obtained for von Neumann algebras. In general $C^*$-algebras we have to m"},"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":"1204.4942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-04-22T21:43:43Z","cross_cats_sorted":["math.FA","math.SP"],"title_canon_sha256":"c164a4adba4d4a38932244df6b4860e26be70cc75e1aebf7c3aec3dd37c1ce2d","abstract_canon_sha256":"ec91e7a58e74513a42b782b277b082d0b5d61df1f9f573c19a0e322d61631403"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:15.125914Z","signature_b64":"wAyEECSch/XFfdHxbZdqzYO3QZElYioGnaevp/DDye3GQ8b+tH30EzgM3ZaOmCQzUlpdpPAwW4daLTtOVCLWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"739780e3fd0129ffccbe25b5d6d3c51e1cea510262adfa68bff83a2eec2b04c5","last_reissued_at":"2026-05-18T03:57:15.125438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:15.125438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identifying derivations through the spectra of their values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.OA","authors_text":"B. Magajna, M. Bre\\v{s}ar, \\v{S}. \\v{S}penko","submitted_at":"2012-04-22T21:43:43Z","abstract_excerpt":"We consider the relationship between derivations $d$ and $g$ of a Banach algebra $B$ that satisfy $\\s(g(x)) \\subseteq \\s(d(x))$ for every $x\\in B$, where $\\s(\\, . \\,)$ stands for the spectrum. It turns out that in some basic situations, say if $B=B(X)$, the only possibilities are that $g=d$, $g=0$, and, if $d$ is an inner derivation implemented by an algebraic element of degree 2, also $g=-d$. The conclusions in more complex classes of algebras are not so simple, but are of a similar spirit. A rather definitive result is obtained for von Neumann algebras. In general $C^*$-algebras we have to m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4942","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":"1204.4942","created_at":"2026-05-18T03:57:15.125509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.4942v1","created_at":"2026-05-18T03:57:15.125509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4942","created_at":"2026-05-18T03:57:15.125509+00:00"},{"alias_kind":"pith_short_12","alias_value":"OOLYBY75AEU7","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OOLYBY75AEU77TF6","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OOLYBY75","created_at":"2026-05-18T12:27:16.716162+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/OOLYBY75AEU77TF6EW25NU6FDY","json":"https://pith.science/pith/OOLYBY75AEU77TF6EW25NU6FDY.json","graph_json":"https://pith.science/api/pith-number/OOLYBY75AEU77TF6EW25NU6FDY/graph.json","events_json":"https://pith.science/api/pith-number/OOLYBY75AEU77TF6EW25NU6FDY/events.json","paper":"https://pith.science/paper/OOLYBY75"},"agent_actions":{"view_html":"https://pith.science/pith/OOLYBY75AEU77TF6EW25NU6FDY","download_json":"https://pith.science/pith/OOLYBY75AEU77TF6EW25NU6FDY.json","view_paper":"https://pith.science/paper/OOLYBY75","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.4942&json=true","fetch_graph":"https://pith.science/api/pith-number/OOLYBY75AEU77TF6EW25NU6FDY/graph.json","fetch_events":"https://pith.science/api/pith-number/OOLYBY75AEU77TF6EW25NU6FDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OOLYBY75AEU77TF6EW25NU6FDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OOLYBY75AEU77TF6EW25NU6FDY/action/storage_attestation","attest_author":"https://pith.science/pith/OOLYBY75AEU77TF6EW25NU6FDY/action/author_attestation","sign_citation":"https://pith.science/pith/OOLYBY75AEU77TF6EW25NU6FDY/action/citation_signature","submit_replication":"https://pith.science/pith/OOLYBY75AEU77TF6EW25NU6FDY/action/replication_record"}},"created_at":"2026-05-18T03:57:15.125509+00:00","updated_at":"2026-05-18T03:57:15.125509+00:00"}