{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KKSIMDFTBE7QJG4HWSUWZ2725X","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":"06fcd8ae15b9c0b6ba61b13bd1b323a53927638378583fcdd32f6968d9e2523e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-17T20:47:25Z","title_canon_sha256":"e0d1833d1b03e2b56d91eb5808d83e41b02837a5ff032d0a32b4f5f7ab7d21f8"},"schema_version":"1.0","source":{"id":"1612.05821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05821","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05821v1","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05821","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"KKSIMDFTBE7Q","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KKSIMDFTBE7QJG4H","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KKSIMDFT","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:22885f4b8b0f91b331d818fd58e73ca989689b7be3792e56476465715e121c1a","target":"graph","created_at":"2026-05-18T00:54:46Z","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":"It is proved that a commutative algebra $A$ of operators in a reflexive real Banach space has an invariant subspace if each operator $T\\in A$ satisfies the condition $$\\|1- \\varepsilon T^2\\|_e \\le 1 + o(\\varepsilon) \\text{ when } \\varepsilon\\searrow 0,$$ where $\\|\\cdot\\|_e$ is the essential norm. This implies the existence of an invariant subspace for every commutative family of essentially selfadjoint operators in a real Hilbert space.","authors_text":"Victor Lomonosov, Victor Shulman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-17T20:47:25Z","title":"Invariant subspaces for commuting operators in a real Banach space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05821","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":"sha256:43bfdd1aac93dedf8eb54c5b53ae58fe1760b5c6e90ca1e8837db52893ecac74","target":"record","created_at":"2026-05-18T00:54:46Z","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":"06fcd8ae15b9c0b6ba61b13bd1b323a53927638378583fcdd32f6968d9e2523e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-17T20:47:25Z","title_canon_sha256":"e0d1833d1b03e2b56d91eb5808d83e41b02837a5ff032d0a32b4f5f7ab7d21f8"},"schema_version":"1.0","source":{"id":"1612.05821","kind":"arxiv","version":1}},"canonical_sha256":"52a4860cb3093f049b87b4a96cebfaedd9ed3ee767403bf14748c2f3cce56f6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52a4860cb3093f049b87b4a96cebfaedd9ed3ee767403bf14748c2f3cce56f6a","first_computed_at":"2026-05-18T00:54:46.572642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:46.572642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LDUp2KmEV/ikncOdnyIRu7GFAG4OWyKwNk9/d6lmAXZH10Vld7YESNjvgfo6+SteYJ3g6RucKCeLgCj8GJJ9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:46.573077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43bfdd1aac93dedf8eb54c5b53ae58fe1760b5c6e90ca1e8837db52893ecac74","sha256:22885f4b8b0f91b331d818fd58e73ca989689b7be3792e56476465715e121c1a"],"state_sha256":"b31ef10da1c2e25057df1c97c22476a1fc6b9270024bc0202ad95aab5fa0deb1"}