{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EDAZH4IDEQKRJ5XL7ABL2BITN5","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":"c19edebe0d316d1ffcee61dd8e9a286933df2cfbe61b6a841d9578dbdca7a5c4","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:06:55Z","title_canon_sha256":"c2f74ee9a257a530b595779c382e31f5cb2537633212fe712276ba68b8c6ef6e"},"schema_version":"1.0","source":{"id":"1802.04092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04092","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04092v1","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04092","created_at":"2026-05-18T00:23:46Z"},{"alias_kind":"pith_short_12","alias_value":"EDAZH4IDEQKR","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EDAZH4IDEQKRJ5XL","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EDAZH4ID","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:e548fc65fdbf942c05b151d1a21b421e4aebbb8b1e6c122ed7c9858c68443ab6","target":"graph","created_at":"2026-05-18T00:23:46Z","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":"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.","authors_text":"Songxiao Li, Yecheng Shi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:06:55Z","title":"Linear combination of composition operators on $H^\\infty$ and the Bloch space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04092","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":"sha256:8a91e6046b1b48cc2fc11a5b07c66972613e9a76680040c6f980357ce9ac2f76","target":"record","created_at":"2026-05-18T00:23:46Z","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":"c19edebe0d316d1ffcee61dd8e9a286933df2cfbe61b6a841d9578dbdca7a5c4","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T15:06:55Z","title_canon_sha256":"c2f74ee9a257a530b595779c382e31f5cb2537633212fe712276ba68b8c6ef6e"},"schema_version":"1.0","source":{"id":"1802.04092","kind":"arxiv","version":1}},"canonical_sha256":"20c193f103241514f6ebf802bd05136f7a500ab0f28e7412ef31ec8bc8ac73f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20c193f103241514f6ebf802bd05136f7a500ab0f28e7412ef31ec8bc8ac73f2","first_computed_at":"2026-05-18T00:23:46.885378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:46.885378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZronHm9O6LsV8HeiHmyL4Y2VnWMZ1JIHGTVu7NE6A5cjj2755RGtIMN7vSfAKFoUxIljScayzOlD8WRvIAz4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:46.885908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a91e6046b1b48cc2fc11a5b07c66972613e9a76680040c6f980357ce9ac2f76","sha256:e548fc65fdbf942c05b151d1a21b421e4aebbb8b1e6c122ed7c9858c68443ab6"],"state_sha256":"b9c7b43fb44e36ca7d74da75fb395877c7fd597a51fc71ef4cac36f8b77d4812"}