{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VDO724NOSVDQDZQ4UHNLVXCEWE","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":"506fcde7746025744e92fd7dd78194e3f603b2bdaee2e22a4be45888998d1cf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-11T13:44:46Z","title_canon_sha256":"8ca11ff1e4b326095dd6c122e8b76ccac4faac3a08e19038c0e0f759b28a7544"},"schema_version":"1.0","source":{"id":"1606.03593","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03593","created_at":"2026-05-18T01:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03593v1","created_at":"2026-05-18T01:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03593","created_at":"2026-05-18T01:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"VDO724NOSVDQ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VDO724NOSVDQDZQ4","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VDO724NO","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:8cd15b10f42b0f99a6c93f5e3d1135fadd755588e50ec7b48bf5289b3b727751","target":"graph","created_at":"2026-05-18T01:12:33Z","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":"Let ${\\mathcal A}$ and ${\\frak A}$ be Banach algebras such that ${\\mathcal A}$ is a Banach ${\\frak A}$-bimodule with compatible actions. We define the product ${\\cal A}\\rtimes{\\frak A}$, which is a strongly splitting Banach algebra extension of ${\\frak A}$ by $\\cal A$. After characterization of the multiplier algebra, topological centre, (maximal) ideals and spectrum of ${\\cal A}\\rtimes{\\frak A}$, we restrict our investigation to the study of semisimplicity, regularity, Arens regularity of ${\\cal A}\\rtimes{\\frak A}$ in relation to that of the algebras $\\cal A$, $\\frak A$ and the action of $\\fr","authors_text":"Hossein Javanshiri, Mehdi Nemati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-11T13:44:46Z","title":"Amalgamated duplication of the Banach algebra $\\bf{\\frak A}$ along a ${\\frak A}$-bimodule ${\\mathcal A}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03593","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":"sha256:7f49333c305378f3f158b3bbcd0d5fdad4c748665fff8fbc7489b0a67411b4f7","target":"record","created_at":"2026-05-18T01:12:33Z","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":"506fcde7746025744e92fd7dd78194e3f603b2bdaee2e22a4be45888998d1cf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-11T13:44:46Z","title_canon_sha256":"8ca11ff1e4b326095dd6c122e8b76ccac4faac3a08e19038c0e0f759b28a7544"},"schema_version":"1.0","source":{"id":"1606.03593","kind":"arxiv","version":1}},"canonical_sha256":"a8ddfd71ae954701e61ca1dabadc44b11b448ff89a7e617d2a40a1f1b1ed743d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8ddfd71ae954701e61ca1dabadc44b11b448ff89a7e617d2a40a1f1b1ed743d","first_computed_at":"2026-05-18T01:12:33.592101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:33.592101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2JoyiLSLgWX0eq/aK5uMrVc8gft7cQeAD3Xy5BjFI1Siv6KulV7SQwiiW3YcNcJUn5DzN+5oYBtGwIYdvWFWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:33.592549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03593","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f49333c305378f3f158b3bbcd0d5fdad4c748665fff8fbc7489b0a67411b4f7","sha256:8cd15b10f42b0f99a6c93f5e3d1135fadd755588e50ec7b48bf5289b3b727751"],"state_sha256":"d4d889e604029fdccc67730ed80337fffeecc4c5d121ea01f087a54731c07ae2"}