{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:26RQSOXJJ2RPSYIIV5T2C6NDB3","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":"3f9b1747a9560e90c47abeed39eea13e57aab1b60403209526c57f6eda0bd2c1","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-16T14:39:29Z","title_canon_sha256":"4eea37c51ea3f80213538b96b2314d72e67c1260ce865d9d3b8dcee55e74e830"},"schema_version":"1.0","source":{"id":"1211.3903","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3903","created_at":"2026-05-18T03:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3903v2","created_at":"2026-05-18T03:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3903","created_at":"2026-05-18T03:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"26RQSOXJJ2RP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"26RQSOXJJ2RPSYII","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"26RQSOXJ","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:361be144f5c20bd0bf8c6db79471da8d07e5f35e693d573383b2c7c5b3ae88a1","target":"graph","created_at":"2026-05-18T03:09:22Z","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 explore a duality between von-Neumann's mean ergodic theorem in von-Neumann algebra and Birkhoff's mean ergodic theorem in the pre-dual Banach space of von-Neumann algebras. Besides improving known mean ergodic theorems on von-Neumann algebras, we prove Birkhoff's mean ergodic theorem for any locally compact second countable amenable group action on the pre-dual Banach space.","authors_text":"Anilesh Mohari","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-16T14:39:29Z","title":"A mean ergodic theorem in von-Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3903","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:a8ebbec984aa9b6bc1ffed0f1dd033f7ce41b7c8ab2ec8313a728b114f10f723","target":"record","created_at":"2026-05-18T03:09:22Z","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":"3f9b1747a9560e90c47abeed39eea13e57aab1b60403209526c57f6eda0bd2c1","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-11-16T14:39:29Z","title_canon_sha256":"4eea37c51ea3f80213538b96b2314d72e67c1260ce865d9d3b8dcee55e74e830"},"schema_version":"1.0","source":{"id":"1211.3903","kind":"arxiv","version":2}},"canonical_sha256":"d7a3093ae94ea2f96108af67a179a30efc9a7eefa3c2aadd5c6e1f54a92c3f86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7a3093ae94ea2f96108af67a179a30efc9a7eefa3c2aadd5c6e1f54a92c3f86","first_computed_at":"2026-05-18T03:09:22.652913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:22.652913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ns5EeGaO2LC3OQjd6/jv2qGoppcALJ1LpDyYMck7QXcZGgi2fb7ybGrVEJrqOtXQmG87pTManNtRh7rKe7LtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:22.653656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3903","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8ebbec984aa9b6bc1ffed0f1dd033f7ce41b7c8ab2ec8313a728b114f10f723","sha256:361be144f5c20bd0bf8c6db79471da8d07e5f35e693d573383b2c7c5b3ae88a1"],"state_sha256":"484e5931a1a5f1b7717a7921fc91c5f3bb72937a09c8f72e1f5c47f300f63be2"}