{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MSLKIBGNBJD5P4WVUTUV55OE6O","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":"f2b67855533efcfa7c95d1602944bfe5d385d0b4d4fc38d2a4ceaf3ffe2eb137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-06T14:37:34Z","title_canon_sha256":"15fdd560be09adaaba5bc1be140bd72d5d89c2f06fbf1a6eaccb904c8a55fa74"},"schema_version":"1.0","source":{"id":"1310.1591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1591","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1591v1","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1591","created_at":"2026-05-18T03:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"MSLKIBGNBJD5","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MSLKIBGNBJD5P4WV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MSLKIBGN","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:766b4eee2d2852fefac4094f9ced22fc210a3939679c73c4c8c3d385a20c7f79","target":"graph","created_at":"2026-05-18T03:11:11Z","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":"In this note we extend some recent results in the space of regular operators. In particular, we provide the following Banach lattice version of a classical result of Kalton: Let $E$ be an atomic Banach lattice with an order continuous norm and $F$ a Banach lattice. Then the following are equivalent: (i) $L^r(E,F)$ contains no copy of $\\ell_\\infty$, \\,\\, (ii) $L^r(E,F)$ contains no copy of $c_0$, \\,\\, (iii) $K^r(E,F)$ contains no copy of $c_0$, \\,\\, (iv) $K^r(E,F)$ is a (projection) band in $L^r(E,F)$, \\,\\, (v) $K^r(E,F)=L^r(E,F)$.","authors_text":"Foivos Xanthos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-06T14:37:34Z","title":"A version of Kalton's theorem for the space of regular operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1591","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":"sha256:1f00605173462a68ba69a7a559cbff60810a7247e1a98009633fd34d3948f8f0","target":"record","created_at":"2026-05-18T03:11:11Z","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":"f2b67855533efcfa7c95d1602944bfe5d385d0b4d4fc38d2a4ceaf3ffe2eb137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-06T14:37:34Z","title_canon_sha256":"15fdd560be09adaaba5bc1be140bd72d5d89c2f06fbf1a6eaccb904c8a55fa74"},"schema_version":"1.0","source":{"id":"1310.1591","kind":"arxiv","version":1}},"canonical_sha256":"6496a404cd0a47d7f2d5a4e95ef5c4f3987fb0e2e308df1fb948e6758dc4c84e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6496a404cd0a47d7f2d5a4e95ef5c4f3987fb0e2e308df1fb948e6758dc4c84e","first_computed_at":"2026-05-18T03:11:11.382406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:11.382406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yivqenNtHPL17xmEBegcoeTWJFp4IM1jxyKf8i05ZrQc8kdLQtJGrarekQjvsFPMV/wV6MUZJj89fKHXd8uBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:11.383271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f00605173462a68ba69a7a559cbff60810a7247e1a98009633fd34d3948f8f0","sha256:766b4eee2d2852fefac4094f9ced22fc210a3939679c73c4c8c3d385a20c7f79"],"state_sha256":"08f2493f40fd54856007d4f142b5bed70fafe555c7ec028ccb6ed9ee4e310934"}