{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WKEYVV2CTHOCXNKI4SDJJPQHWX","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":"a25f72f7f7f0ea61a1d60733cbf90ef2b9e4a936036b49255d0551b26f435c3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-15T15:36:57Z","title_canon_sha256":"6a6aba72785885544bb3ec53486a5220fd1c7a4e0a66df318ccdd5345a68f888"},"schema_version":"1.0","source":{"id":"1012.3362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3362","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3362v1","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3362","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"pith_short_12","alias_value":"WKEYVV2CTHOC","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"WKEYVV2CTHOCXNKI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"WKEYVV2C","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:c50e7df47a9a4ab849547dc71b0431f6b78e64692d330cf59e0c922bee37cc1f","target":"graph","created_at":"2026-05-18T04:33:17Z","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":"Using principles of the theory of smoothness spaces we give systematic constructions of scales of inverse-closed subalgebras of a given Banach algebra with the action of a d-parameter automorphism group. In particular we obtain the inverse-closedness of Besov algebras, Bessel potential algebras and approximation algebras of polynomial order in their defining algebra. By a proper choice of the group action these general results can be applied to algebras of infinite matrices and yield inverse-closed subalgebras of matrices with off-diagonal decay of polynomial order. Besides alternative proofs ","authors_text":"Andreas Klotz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-15T15:36:57Z","title":"Spectral Invariance of Besov-Bessel Subalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3362","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:b4dd037dce57799e48a31ec000dd82eefb3254c3df80a306d1b52e40126c3d51","target":"record","created_at":"2026-05-18T04:33:17Z","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":"a25f72f7f7f0ea61a1d60733cbf90ef2b9e4a936036b49255d0551b26f435c3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-15T15:36:57Z","title_canon_sha256":"6a6aba72785885544bb3ec53486a5220fd1c7a4e0a66df318ccdd5345a68f888"},"schema_version":"1.0","source":{"id":"1012.3362","kind":"arxiv","version":1}},"canonical_sha256":"b2898ad74299dc2bb548e48694be07b5d0fc223acc68c02ac30677963c8a2891","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2898ad74299dc2bb548e48694be07b5d0fc223acc68c02ac30677963c8a2891","first_computed_at":"2026-05-18T04:33:17.019559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:17.019559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SgWoX3K6UAWNtxoUIAqpazHDzCYIhwOngn/rKfR234yceIjFfRLpoa/oAbZjGnCUHLXKV5uvyyPn3z8rgpvEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:17.020257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4dd037dce57799e48a31ec000dd82eefb3254c3df80a306d1b52e40126c3d51","sha256:c50e7df47a9a4ab849547dc71b0431f6b78e64692d330cf59e0c922bee37cc1f"],"state_sha256":"9d20702b56d945d1b7d87856fa95612f049ab95ecdda580869ae2f206259e8cc"}