{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3LAG4TES2FNGMTXMHZEHFNCNV5","short_pith_number":"pith:3LAG4TES","schema_version":"1.0","canonical_sha256":"dac06e4c92d15a664eec3e4872b44daf74b97141350bac2f162263b527dbf9ba","source":{"kind":"arxiv","id":"1808.10372","version":1},"attestation_state":"computed","paper":{"title":"Algebras of Toeplitz operators on the $n$-dimensional unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Nikolai Vasilevski, Raffael Hagger, Wolfram Bauer","submitted_at":"2018-08-30T16:00:25Z","abstract_excerpt":"We study $C^*$-algebras generated by Toeplitz operators acting on the standard weighted Bergman space $\\mathcal{A}_{\\lambda}^2(\\mathbb{B}^n)$ over the unit ball $\\mathbb{B}^n$ in $\\mathbb{C}^n$. The symbols $f_{ac}$ of generating operators are assumed to be of a certain product type. By choosing $a$ and $c$ in different function algebras $\\mathcal{S}_a$ and $\\mathcal{S}_c$ over lower dimensional unit balls $\\mathbb{B}^{\\ell}$ and $\\mathbb{B}^{n-\\ell}$, respectively, and by assuming the invariance of $a\\in \\mathcal{S}_a$ under some torus action we obtain $C^*$-algebras $\\boldsymbol{\\mathcal{T}}"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.10372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-08-30T16:00:25Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"15ed846e57b4d61e5878295700136613aee8c6713d9187d51ae86e6a3919c614","abstract_canon_sha256":"49e35885fa7f3bd41682e7c5736dd886cc72a483d1bd35eb73579aef5667236c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:48.986963Z","signature_b64":"HsPM7oqF0N7lX/+BiFJxatqu1QfGkFQqTiR1pJmAoxv66+oaOzWaqimUP9KOOA/jVwEpMswQlE/ysndzaimgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dac06e4c92d15a664eec3e4872b44daf74b97141350bac2f162263b527dbf9ba","last_reissued_at":"2026-05-18T00:06:48.986451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:48.986451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebras of Toeplitz operators on the $n$-dimensional unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Nikolai Vasilevski, Raffael Hagger, Wolfram Bauer","submitted_at":"2018-08-30T16:00:25Z","abstract_excerpt":"We study $C^*$-algebras generated by Toeplitz operators acting on the standard weighted Bergman space $\\mathcal{A}_{\\lambda}^2(\\mathbb{B}^n)$ over the unit ball $\\mathbb{B}^n$ in $\\mathbb{C}^n$. The symbols $f_{ac}$ of generating operators are assumed to be of a certain product type. By choosing $a$ and $c$ in different function algebras $\\mathcal{S}_a$ and $\\mathcal{S}_c$ over lower dimensional unit balls $\\mathbb{B}^{\\ell}$ and $\\mathbb{B}^{n-\\ell}$, respectively, and by assuming the invariance of $a\\in \\mathcal{S}_a$ under some torus action we obtain $C^*$-algebras $\\boldsymbol{\\mathcal{T}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10372","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.10372","created_at":"2026-05-18T00:06:48.986538+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.10372v1","created_at":"2026-05-18T00:06:48.986538+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10372","created_at":"2026-05-18T00:06:48.986538+00:00"},{"alias_kind":"pith_short_12","alias_value":"3LAG4TES2FNG","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3LAG4TES2FNGMTXM","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3LAG4TES","created_at":"2026-05-18T12:32:02.567920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5","json":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5.json","graph_json":"https://pith.science/api/pith-number/3LAG4TES2FNGMTXMHZEHFNCNV5/graph.json","events_json":"https://pith.science/api/pith-number/3LAG4TES2FNGMTXMHZEHFNCNV5/events.json","paper":"https://pith.science/paper/3LAG4TES"},"agent_actions":{"view_html":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5","download_json":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5.json","view_paper":"https://pith.science/paper/3LAG4TES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.10372&json=true","fetch_graph":"https://pith.science/api/pith-number/3LAG4TES2FNGMTXMHZEHFNCNV5/graph.json","fetch_events":"https://pith.science/api/pith-number/3LAG4TES2FNGMTXMHZEHFNCNV5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5/action/storage_attestation","attest_author":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5/action/author_attestation","sign_citation":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5/action/citation_signature","submit_replication":"https://pith.science/pith/3LAG4TES2FNGMTXMHZEHFNCNV5/action/replication_record"}},"created_at":"2026-05-18T00:06:48.986538+00:00","updated_at":"2026-05-18T00:06:48.986538+00:00"}