{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JI3S5TT4ABIZSYBQ7FVT7XVC2B","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":"1c0bff9be0e6bbe47a71dc798bcbdcfaf9df41c2dbdb71da8b333516c9b571a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-21T19:06:26Z","title_canon_sha256":"c42b0964b1aab6f6720b10718d74264a0fec77bbf3b58b9a5e554201722948f5"},"schema_version":"1.0","source":{"id":"1706.07088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07088","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07088v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07088","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"JI3S5TT4ABIZ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JI3S5TT4ABIZSYBQ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JI3S5TT4","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:8d2af04654940720ffa9db5f014ba1820dd5c23f37baee7603c58190b32ab3ae","target":"graph","created_at":"2026-05-18T00:41:52Z","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 shall develop two notions of pointwise amenability, namely pointwise Connes amenability and pointwise $w^*$-approximate Connes amenability, for dual Banach algebras which take the $w^*$-topology into account. We shall study these concepts for the Banach sequence algebras $\\ell^1(\\omega)$ and the weighted semigroup algebras $ \\ell^{1}(\\mathbb{N}_{\\wedge},\\omega)$. For a weight $\\omega$ on a discrete semigroup $S$, we shall investigate pointwise amenability/Connes amenability of $\\ell^1(S,\\omega)$ in terms of diagonals.","authors_text":"Amin Mahmoodi, Mannane Shakeri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-21T19:06:26Z","title":"Pointwise amenability for dual Banach algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07088","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:d680b633e66f8f52c080665d39e69ec3a5d8dde0404c29e5c130833758a6de6b","target":"record","created_at":"2026-05-18T00:41:52Z","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":"1c0bff9be0e6bbe47a71dc798bcbdcfaf9df41c2dbdb71da8b333516c9b571a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-21T19:06:26Z","title_canon_sha256":"c42b0964b1aab6f6720b10718d74264a0fec77bbf3b58b9a5e554201722948f5"},"schema_version":"1.0","source":{"id":"1706.07088","kind":"arxiv","version":1}},"canonical_sha256":"4a372ece7c0051996030f96b3fdea2d0589d7f8d25740e7032a2b05db67730ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a372ece7c0051996030f96b3fdea2d0589d7f8d25740e7032a2b05db67730ef","first_computed_at":"2026-05-18T00:41:52.652921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:52.652921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NyBvnIjdMKf83Oi8he8wqA2g8BO1rBNEatUNJ12/a4ARYLH/TnhMjgr+74xrZT1O9HbFjT4lsVXBATF1WawsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:52.653589Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d680b633e66f8f52c080665d39e69ec3a5d8dde0404c29e5c130833758a6de6b","sha256:8d2af04654940720ffa9db5f014ba1820dd5c23f37baee7603c58190b32ab3ae"],"state_sha256":"ccd7c7828b7bb8de44b1f476e2158b32d3cc51f2471c1879a44f2414f18009d9"}