{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:TU3BLZNQ6TUN3FVTYTFIGTCE4Q","short_pith_number":"pith:TU3BLZNQ","schema_version":"1.0","canonical_sha256":"9d3615e5b0f4e8dd96b3c4ca834c44e43661fafaa8a5d9f402950281168505ef","source":{"kind":"arxiv","id":"math/9404210","version":1},"attestation_state":"computed","paper":{"title":"Orlicz property of operator spaces and eigenvalue estimates","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marius Junge","submitted_at":"1994-04-14T16:07:37Z","abstract_excerpt":"As is well known absolute convergence and unconditional convergence for series are equivalent only in finite dimensional Banach spaces. Replacing the classical notion of absolutely summing operators by the notion of 1 summing operators \\[ \\summ_k || Tx_k || \\leq c || \\summ_k e_k \\otimes x_k ||_{\\ell_1\\otimes_{min}E}\\] in the category of operator spaces, it turns out that there are quite different interesting examples of 1 summing operator spaces. Moreover, the eigenvalues of a composition $TS$ decreases of order $n^{\\frac{1}{q}}$ for all operators $S$ factorizing completely through a commutati"},"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":"math/9404210","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1994-04-14T16:07:37Z","cross_cats_sorted":[],"title_canon_sha256":"66df491e49dc9d2d55802df10786a3e0bb648729fe713cc4151a3efba30e9675","abstract_canon_sha256":"7c7d445c5cf675b34dfb9803040f03311138d7748217ce797e7804285aa50157"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.498554Z","signature_b64":"nfGkAoGo1+roki9qWcst5XJlQZULuPrFkol80ICP4DHMo8IU05ciZMNc1ZAYAwQbS7j7UGCc6l6ZU72VUr6MDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d3615e5b0f4e8dd96b3c4ca834c44e43661fafaa8a5d9f402950281168505ef","last_reissued_at":"2026-05-18T01:05:51.498133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.498133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orlicz property of operator spaces and eigenvalue estimates","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marius Junge","submitted_at":"1994-04-14T16:07:37Z","abstract_excerpt":"As is well known absolute convergence and unconditional convergence for series are equivalent only in finite dimensional Banach spaces. Replacing the classical notion of absolutely summing operators by the notion of 1 summing operators \\[ \\summ_k || Tx_k || \\leq c || \\summ_k e_k \\otimes x_k ||_{\\ell_1\\otimes_{min}E}\\] in the category of operator spaces, it turns out that there are quite different interesting examples of 1 summing operator spaces. Moreover, the eigenvalues of a composition $TS$ decreases of order $n^{\\frac{1}{q}}$ for all operators $S$ factorizing completely through a commutati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9404210","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":"math/9404210","created_at":"2026-05-18T01:05:51.498198+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9404210v1","created_at":"2026-05-18T01:05:51.498198+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9404210","created_at":"2026-05-18T01:05:51.498198+00:00"},{"alias_kind":"pith_short_12","alias_value":"TU3BLZNQ6TUN","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"TU3BLZNQ6TUN3FVT","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"TU3BLZNQ","created_at":"2026-05-18T12:25:47.102015+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/TU3BLZNQ6TUN3FVTYTFIGTCE4Q","json":"https://pith.science/pith/TU3BLZNQ6TUN3FVTYTFIGTCE4Q.json","graph_json":"https://pith.science/api/pith-number/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/graph.json","events_json":"https://pith.science/api/pith-number/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/events.json","paper":"https://pith.science/paper/TU3BLZNQ"},"agent_actions":{"view_html":"https://pith.science/pith/TU3BLZNQ6TUN3FVTYTFIGTCE4Q","download_json":"https://pith.science/pith/TU3BLZNQ6TUN3FVTYTFIGTCE4Q.json","view_paper":"https://pith.science/paper/TU3BLZNQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9404210&json=true","fetch_graph":"https://pith.science/api/pith-number/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/graph.json","fetch_events":"https://pith.science/api/pith-number/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/action/storage_attestation","attest_author":"https://pith.science/pith/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/action/author_attestation","sign_citation":"https://pith.science/pith/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/action/citation_signature","submit_replication":"https://pith.science/pith/TU3BLZNQ6TUN3FVTYTFIGTCE4Q/action/replication_record"}},"created_at":"2026-05-18T01:05:51.498198+00:00","updated_at":"2026-05-18T01:05:51.498198+00:00"}