{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WC2RM4IT7JRS3V4UTIF4EWKLFH","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":"f2978bea725b993fc51903f576491b3e95027dc84ef1b759a4b039d66f2654e8","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-12-07T02:41:23Z","title_canon_sha256":"1555f9d487af45dd430d27e444597bd0e1cc4529750de4a9ba2caf416acd21fd"},"schema_version":"1.0","source":{"id":"2412.05509","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.05509","created_at":"2026-05-26T01:03:09Z"},{"alias_kind":"arxiv_version","alias_value":"2412.05509v4","created_at":"2026-05-26T01:03:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.05509","created_at":"2026-05-26T01:03:09Z"},{"alias_kind":"pith_short_12","alias_value":"WC2RM4IT7JRS","created_at":"2026-05-26T01:03:09Z"},{"alias_kind":"pith_short_16","alias_value":"WC2RM4IT7JRS3V4U","created_at":"2026-05-26T01:03:09Z"},{"alias_kind":"pith_short_8","alias_value":"WC2RM4IT","created_at":"2026-05-26T01:03:09Z"}],"graph_snapshots":[{"event_id":"sha256:ed909e3b313701105ee63103b53dd9f48521e2731bb141d69c74ab028a15025d","target":"graph","created_at":"2026-05-26T01:03:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.05509/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is a sequel to our work in \\cite{Das-Mundayadan}. Here, we primarily study the dynamics of the adjoint of a weighted forward shift operator $F_w$ on the analytic function space $\\ell^p_{a,b}$ having a normalized Schauder basis of the form $\\{(a_n+b_nz)z^n:~n \\geq 0\\}$. We obtain sufficient conditions for $F_w$ to be continuous, and show, under certain conditions, that the operator $F_w$ is similar to a compact perturbation of a weighted forward shift on $\\ell^p(\\mathbb{N}_0)$. This also allows us to obtain the essential spectrum of $F_w$. Further, we study when the adjoint $F_w^*$ i","authors_text":"Aneesh Mundayadan, Bibhash Kumar Das","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-12-07T02:41:23Z","title":"Linear dynamics of the adjoint of a unilateral weighted shift operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.05509","kind":"arxiv","version":4},"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":"sha256:5145a48831750df49057be3bd5fc3689b6196ad0fa21d328d00b270b4270ea91","target":"record","created_at":"2026-05-26T01:03:09Z","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":"f2978bea725b993fc51903f576491b3e95027dc84ef1b759a4b039d66f2654e8","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2024-12-07T02:41:23Z","title_canon_sha256":"1555f9d487af45dd430d27e444597bd0e1cc4529750de4a9ba2caf416acd21fd"},"schema_version":"1.0","source":{"id":"2412.05509","kind":"arxiv","version":4}},"canonical_sha256":"b0b5167113fa632dd7949a0bc2594b29df11b554513a1efc0b143eb59fd3f147","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b0b5167113fa632dd7949a0bc2594b29df11b554513a1efc0b143eb59fd3f147","first_computed_at":"2026-05-26T01:03:09.738665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:09.738665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aGtw32zfypMbJsETuCrN4rsVMZkhiHxkx4thOJM8EybN+JL3tAWiAY512314uzQyhyoKGjKkhT5jtNn75haCBA==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:09.739439Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.05509","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5145a48831750df49057be3bd5fc3689b6196ad0fa21d328d00b270b4270ea91","sha256:ed909e3b313701105ee63103b53dd9f48521e2731bb141d69c74ab028a15025d"],"state_sha256":"a633c8f8910d17ed54cabda9ef75397c7cf91c5cb01fdb0aef261cedc4f88d6a"}