{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BZ43CDQOVICGLZZ427JTC7HRKR","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":"8d1af614ef0d8763d26eda2bdb85f8baf1d5c36b858b5a4242c92a7363442c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-26T09:19:02Z","title_canon_sha256":"a7b957980c63ccb2d97db3b98a9b75b7fb22c77b437c5157bbb65491505ed20a"},"schema_version":"1.0","source":{"id":"1302.6369","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6369","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6369v2","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6369","created_at":"2026-05-18T02:17:52Z"},{"alias_kind":"pith_short_12","alias_value":"BZ43CDQOVICG","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BZ43CDQOVICGLZZ4","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BZ43CDQO","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:29a0dcf416c9fbd563d9fde237a62bb16661b413967426b1549f2bfca76b6b1e","target":"graph","created_at":"2026-05-18T02:17:52Z","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":"We show that the dual to any subspace of $c_0(\\Gamma)$ has the strongest possible quantitative version of the Schur property. Further, we establish relationship between the quantitative Schur property and quantitative versions of the Dunford-Pettis property. Finally, we apply these results to show, in particular, that any subspace of the space of compact operators on $\\ell_p$ ($1<p<\\infty$) with Dunford-Pettis property satisfies automatically both its quantitative versions.","authors_text":"Ji\\v{r}\\'i Spurn\\'y, Ond\\v{r}ej F.K. Kalenda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-26T09:19:02Z","title":"On quantitative Schur and Dunford-Pettis properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6369","kind":"arxiv","version":2},"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:ba394f211b510cc41d39397a9feb0f69a55309a63b52376ac066ea847f72c66e","target":"record","created_at":"2026-05-18T02:17:52Z","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":"8d1af614ef0d8763d26eda2bdb85f8baf1d5c36b858b5a4242c92a7363442c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-26T09:19:02Z","title_canon_sha256":"a7b957980c63ccb2d97db3b98a9b75b7fb22c77b437c5157bbb65491505ed20a"},"schema_version":"1.0","source":{"id":"1302.6369","kind":"arxiv","version":2}},"canonical_sha256":"0e79b10e0eaa0465e73cd7d3317cf15460ae25b389e50bcdea74ab5dcd20c900","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e79b10e0eaa0465e73cd7d3317cf15460ae25b389e50bcdea74ab5dcd20c900","first_computed_at":"2026-05-18T02:17:52.464157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:52.464157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tQ+Sxc8MfhrWcGEZzsGRO4+zXmC8ZX0g03CiJHHDYPvyXJBSkX0MVNBZLoVc4QU1jEoV9Yrg7JCbyECtry36Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:52.464971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6369","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba394f211b510cc41d39397a9feb0f69a55309a63b52376ac066ea847f72c66e","sha256:29a0dcf416c9fbd563d9fde237a62bb16661b413967426b1549f2bfca76b6b1e"],"state_sha256":"181cbd41a96c45641036bda1a4b0c62768f1c6df030e77c6fbb9644055e51167"}