{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UXO6SHTIIZUZILYN5OD74YL2PC","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":"04cbcf08a1aa935a9daab7aee000d35165f9dd6f5af1f70664ec6bf8ed722624","cross_cats_sorted":["math.FA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-08T19:33:06Z","title_canon_sha256":"8f6eff108b0dafb55a4e6a677b3936cf9a377cf8db296a55f9049cced0e79ecf"},"schema_version":"1.0","source":{"id":"1307.2210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2210","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2210v1","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2210","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"UXO6SHTIIZUZ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UXO6SHTIIZUZILYN","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UXO6SHTI","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:d9db3000655d3b1c2acad82367ec4d3193f4111067cc01ed6f243696317461c9","target":"graph","created_at":"2026-05-18T03:19:02Z","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 consider a Banach algebra $A$ with the property that, roughly speaking, sufficiently many irreducible representations of $A$ on nontrivial Banach spaces do not vanish on all square zero elements. The class of Banach algebras with this property turns out to be quite large -- it includes $C^*$-algebras, group algebras on arbitrary locally compact groups, commutative algebras, $L(X)$ for any Banach space $X$, and various other examples. Our main result states that every derivation of $A$ that preserves the set of quasinilpotent elements has its range in the radical of $A$.","authors_text":"A. R. Villena, J. Alaminos, J. Extremera, M. Bre\\v{s}ar, \\v{S}. \\v{S}penko","cross_cats":["math.FA","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-08T19:33:06Z","title":"Derivations preserving quasinilpotent elements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2210","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:ff88f29ed7c27b1d6b3a68a5ab31d55b5523d05292bd5cfff6d273a2914c7a55","target":"record","created_at":"2026-05-18T03:19:02Z","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":"04cbcf08a1aa935a9daab7aee000d35165f9dd6f5af1f70664ec6bf8ed722624","cross_cats_sorted":["math.FA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-07-08T19:33:06Z","title_canon_sha256":"8f6eff108b0dafb55a4e6a677b3936cf9a377cf8db296a55f9049cced0e79ecf"},"schema_version":"1.0","source":{"id":"1307.2210","kind":"arxiv","version":1}},"canonical_sha256":"a5dde91e684669942f0deb87fe617a788986fa4830c96919b3c98c7b9cb1d658","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5dde91e684669942f0deb87fe617a788986fa4830c96919b3c98c7b9cb1d658","first_computed_at":"2026-05-18T03:19:02.077587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:02.077587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xt77ycTtBsIRu3EAsyVrpasY9TdgWMFVGWSpN6GrfWsUm35MgGcjdBXeNKG4V2HKdpZbiqX3GPGnVbP46reWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:02.078097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff88f29ed7c27b1d6b3a68a5ab31d55b5523d05292bd5cfff6d273a2914c7a55","sha256:d9db3000655d3b1c2acad82367ec4d3193f4111067cc01ed6f243696317461c9"],"state_sha256":"14ef957d67aa11b609371940a95e525bcebf61c148481d9c2606dcabe925690b"}