{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EDAZH4IDEQKRJ5XL7ABL2BITN5","short_pith_number":"pith:EDAZH4ID","schema_version":"1.0","canonical_sha256":"20c193f103241514f6ebf802bd05136f7a500ab0f28e7412ef31ec8bc8ac73f2","source":{"kind":"arxiv","id":"1802.04092","version":1},"attestation_state":"computed","paper":{"title":"Linear combination of composition operators on $H^\\infty$ and the Bloch space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Songxiao Li, Yecheng Shi","submitted_at":"2018-02-12T15:06:55Z","abstract_excerpt":"Let $\\lambda_i (i=1,...,k)$ be any nonzero complex scalars and $\\varphi_i (i=1,..,k)$ be any analytic self-maps of the unit disk $\\mathbb{D}$. We show that the operator $\\sum_{i=1}^k\\lambda_iC_{\\varphi_i}$ is compact on the Bloch space $\\mathcal{B}$ if and only if\n  $$\\lim_{n\\to\\infty}\\|\\lambda_1\\varphi_1^n+\\lambda_2\\varphi_2^n+...+\\lambda_k\\varphi_k^n\\|_{\\mathcal{B}}=0.$$ We also study the linear combination of composition operators on the Banach algebra of bounded analytic functions."},"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":"1802.04092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:06:55Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c2f74ee9a257a530b595779c382e31f5cb2537633212fe712276ba68b8c6ef6e","abstract_canon_sha256":"c19edebe0d316d1ffcee61dd8e9a286933df2cfbe61b6a841d9578dbdca7a5c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:46.885908Z","signature_b64":"ZronHm9O6LsV8HeiHmyL4Y2VnWMZ1JIHGTVu7NE6A5cjj2755RGtIMN7vSfAKFoUxIljScayzOlD8WRvIAz4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20c193f103241514f6ebf802bd05136f7a500ab0f28e7412ef31ec8bc8ac73f2","last_reissued_at":"2026-05-18T00:23:46.885378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:46.885378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear combination of composition operators on $H^\\infty$ and the Bloch space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Songxiao Li, Yecheng Shi","submitted_at":"2018-02-12T15:06:55Z","abstract_excerpt":"Let $\\lambda_i (i=1,...,k)$ be any nonzero complex scalars and $\\varphi_i (i=1,..,k)$ be any analytic self-maps of the unit disk $\\mathbb{D}$. We show that the operator $\\sum_{i=1}^k\\lambda_iC_{\\varphi_i}$ is compact on the Bloch space $\\mathcal{B}$ if and only if\n  $$\\lim_{n\\to\\infty}\\|\\lambda_1\\varphi_1^n+\\lambda_2\\varphi_2^n+...+\\lambda_k\\varphi_k^n\\|_{\\mathcal{B}}=0.$$ We also study the linear combination of composition operators on the Banach algebra of bounded analytic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04092","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":"1802.04092","created_at":"2026-05-18T00:23:46.885455+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.04092v1","created_at":"2026-05-18T00:23:46.885455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04092","created_at":"2026-05-18T00:23:46.885455+00:00"},{"alias_kind":"pith_short_12","alias_value":"EDAZH4IDEQKR","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EDAZH4IDEQKRJ5XL","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EDAZH4ID","created_at":"2026-05-18T12:32:22.470017+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/EDAZH4IDEQKRJ5XL7ABL2BITN5","json":"https://pith.science/pith/EDAZH4IDEQKRJ5XL7ABL2BITN5.json","graph_json":"https://pith.science/api/pith-number/EDAZH4IDEQKRJ5XL7ABL2BITN5/graph.json","events_json":"https://pith.science/api/pith-number/EDAZH4IDEQKRJ5XL7ABL2BITN5/events.json","paper":"https://pith.science/paper/EDAZH4ID"},"agent_actions":{"view_html":"https://pith.science/pith/EDAZH4IDEQKRJ5XL7ABL2BITN5","download_json":"https://pith.science/pith/EDAZH4IDEQKRJ5XL7ABL2BITN5.json","view_paper":"https://pith.science/paper/EDAZH4ID","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.04092&json=true","fetch_graph":"https://pith.science/api/pith-number/EDAZH4IDEQKRJ5XL7ABL2BITN5/graph.json","fetch_events":"https://pith.science/api/pith-number/EDAZH4IDEQKRJ5XL7ABL2BITN5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EDAZH4IDEQKRJ5XL7ABL2BITN5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EDAZH4IDEQKRJ5XL7ABL2BITN5/action/storage_attestation","attest_author":"https://pith.science/pith/EDAZH4IDEQKRJ5XL7ABL2BITN5/action/author_attestation","sign_citation":"https://pith.science/pith/EDAZH4IDEQKRJ5XL7ABL2BITN5/action/citation_signature","submit_replication":"https://pith.science/pith/EDAZH4IDEQKRJ5XL7ABL2BITN5/action/replication_record"}},"created_at":"2026-05-18T00:23:46.885455+00:00","updated_at":"2026-05-18T00:23:46.885455+00:00"}