{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YPWXIQL6NZGZ5YOJR5VU3AJXE7","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":"895a32fef412ada08e57ba4ae5ef258a19aa5f102fb31748c65bff4f57686efc","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-03-28T09:29:44Z","title_canon_sha256":"35ef15182082bff8cf6c37a01ffa67ed27dbfd4289f65f6e5df67dbd248ecaec"},"schema_version":"1.0","source":{"id":"1803.10483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10483","created_at":"2026-05-18T00:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10483v1","created_at":"2026-05-18T00:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10483","created_at":"2026-05-18T00:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"YPWXIQL6NZGZ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YPWXIQL6NZGZ5YOJ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YPWXIQL6","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:627d79e043ee85fcab9c08bf677e61c2f09a714de67ce16fd08b27dca7e2f630","target":"graph","created_at":"2026-05-18T00:19:55Z","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":"The aim of the present work is to study the Riesz decomposition relative to a C*-algebra homomorphism T : A --> B. We prove that under some conditions on T, T-Riesz elements can be decomposed into the sum of almost T-null element and quasi-nilpotent element. Also the so-called polyno- mial T-Riesz and generalized T-Riesz decompositions will be discussed.","authors_text":"Abdelaziz Tajmouati, Abdeslam El Bakkali, Safae Alaoui Chrifi","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-03-28T09:29:44Z","title":"Riesz Decomposition Relative to C*-Algebra Homomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10483","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":"sha256:415a1846956ae57b084772b0b908f3d39b712c40838856e595add98ea15a0b67","target":"record","created_at":"2026-05-18T00:19:55Z","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":"895a32fef412ada08e57ba4ae5ef258a19aa5f102fb31748c65bff4f57686efc","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-03-28T09:29:44Z","title_canon_sha256":"35ef15182082bff8cf6c37a01ffa67ed27dbfd4289f65f6e5df67dbd248ecaec"},"schema_version":"1.0","source":{"id":"1803.10483","kind":"arxiv","version":1}},"canonical_sha256":"c3ed74417e6e4d9ee1c98f6b4d813727f656385a0ffbf031ea4ee596c62731d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3ed74417e6e4d9ee1c98f6b4d813727f656385a0ffbf031ea4ee596c62731d0","first_computed_at":"2026-05-18T00:19:55.225936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:55.225936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yVONIKSO4lIOFDqVb04JxhCaKM/xiY71bQuoLN17llnUFV83AmAShhDELNAb/jKBkD3W1Adq9F6SrU75t/ZlCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:55.226680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:415a1846956ae57b084772b0b908f3d39b712c40838856e595add98ea15a0b67","sha256:627d79e043ee85fcab9c08bf677e61c2f09a714de67ce16fd08b27dca7e2f630"],"state_sha256":"1cda545113f7ddd7fda31e4345e9b218d69c23376abf9dbb8c6a24d8b71e5d4c"}