{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KB3T7W4FMGTZQMQUBX5IFYTKKK","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":"b2c3e310ea7b645f6121c452ba8da41fda8fbac9aa38e27bcadf5978222a4bfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-17T15:35:20Z","title_canon_sha256":"39760544266ce24398287f7123132c87e9fddc6ee052825b0d9d7d79cd27c0d2"},"schema_version":"1.0","source":{"id":"1201.3531","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3531","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3531v2","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3531","created_at":"2026-05-18T03:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"KB3T7W4FMGTZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KB3T7W4FMGTZQMQU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KB3T7W4F","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:1510dc9371a68e86c8e1caa35fefd4265f73c70132b9c3d73285926fee6c8dd3","target":"graph","created_at":"2026-05-18T03:15:43Z","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":"Given a positive, irreducible and bounded C_0-semigroup on a Banach lattice with order continuous norm, we prove that the peripheral point spectrum of its generator is trivial whenever one of its operators dominates a non-trivial compact or kernel operator. For a discrete semigroup, i.e. for powers of a single operator T, we show that the point spectrum of some power T^k intersects the unit circle at most in 1. As a consequence, we obtain a sufficient condition for strong convergence of the C_0-semigroup and for a subsequence of the powers of T, respectively.","authors_text":"Moritz Gerlach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-17T15:35:20Z","title":"On the peripheral point spectrum and the asymptotic behavior of irreducible semigroups of Harris operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3531","kind":"arxiv","version":2},"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:c1678ab221dfd25f6a04dc25317d8da0fd4c3e29f67c00a5172ee913666cdb5f","target":"record","created_at":"2026-05-18T03:15:43Z","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":"b2c3e310ea7b645f6121c452ba8da41fda8fbac9aa38e27bcadf5978222a4bfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-17T15:35:20Z","title_canon_sha256":"39760544266ce24398287f7123132c87e9fddc6ee052825b0d9d7d79cd27c0d2"},"schema_version":"1.0","source":{"id":"1201.3531","kind":"arxiv","version":2}},"canonical_sha256":"50773fdb8561a79832140dfa82e26a52b725970822c8d4d1db3a166f7a95d076","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50773fdb8561a79832140dfa82e26a52b725970822c8d4d1db3a166f7a95d076","first_computed_at":"2026-05-18T03:15:43.996699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:43.996699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TreWYMU6TKkAXRaF0FT41Nuzpc3hItPSyY2IznVaw1j5bHXJUencKEB08x6ZC23I5mxx/2sf7RYJ3UAHLjolBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:43.997194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3531","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1678ab221dfd25f6a04dc25317d8da0fd4c3e29f67c00a5172ee913666cdb5f","sha256:1510dc9371a68e86c8e1caa35fefd4265f73c70132b9c3d73285926fee6c8dd3"],"state_sha256":"13fc7678440ba94e87613e134e020f056b88e6849b8499a9073f5a523f3fffa1"}