{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TL7ZR5DAN7BE23S577K5VCK6E6","short_pith_number":"pith:TL7ZR5DA","schema_version":"1.0","canonical_sha256":"9aff98f4606fc24d6e5dffd5da895e27bbc153f29f54b27c1212ff26f2e4186b","source":{"kind":"arxiv","id":"1808.03169","version":1},"attestation_state":"computed","paper":{"title":"On the bounded approximation property on subspaces of $\\ell_p$ when $0<p<1$ and related issues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"F\\'elix Cabello S\\'anchez, Jes\\'us M. F. Castillo, Yolanda Moreno","submitted_at":"2018-08-09T13:57:29Z","abstract_excerpt":"This paper studies the bounded approximation property (BAP) in quasi Banach spaces. In the first part of the paper we show that the kernel of any surjective operator $\\ell_p\\to X$ has the BAP when $X$ has it and $0<p\\leq 1$, which is an analogue of the corresponding result of Lusky for Banach spaces. We then obtain and study nonlocally convex versions of the Kadec-Pe\\l czy\\'nski-Wojtaszczyk complementably universal spaces for Banach spaces with the BAP."},"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":"1808.03169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-09T13:57:29Z","cross_cats_sorted":[],"title_canon_sha256":"70e5f8866fcc8a2bde7e4ed34a0f7803701e73548912a81266d552d66b1d94c4","abstract_canon_sha256":"1489341fe214ffa40992683e9bd4a978e7c7554f80786696d8898a53eefaef2a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:30.005971Z","signature_b64":"tzDeCr/Y0IqDJK8T9fWWJiOxpzSNKUwE7jD/IaXjxICqZgzPxBpS7/JohoJn5hsVNjwekA9u7IVNokji93jFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aff98f4606fc24d6e5dffd5da895e27bbc153f29f54b27c1212ff26f2e4186b","last_reissued_at":"2026-05-18T00:08:30.005462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:30.005462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the bounded approximation property on subspaces of $\\ell_p$ when $0<p<1$ and related issues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"F\\'elix Cabello S\\'anchez, Jes\\'us M. F. Castillo, Yolanda Moreno","submitted_at":"2018-08-09T13:57:29Z","abstract_excerpt":"This paper studies the bounded approximation property (BAP) in quasi Banach spaces. In the first part of the paper we show that the kernel of any surjective operator $\\ell_p\\to X$ has the BAP when $X$ has it and $0<p\\leq 1$, which is an analogue of the corresponding result of Lusky for Banach spaces. We then obtain and study nonlocally convex versions of the Kadec-Pe\\l czy\\'nski-Wojtaszczyk complementably universal spaces for Banach spaces with the BAP."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03169","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":"1808.03169","created_at":"2026-05-18T00:08:30.005535+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.03169v1","created_at":"2026-05-18T00:08:30.005535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03169","created_at":"2026-05-18T00:08:30.005535+00:00"},{"alias_kind":"pith_short_12","alias_value":"TL7ZR5DAN7BE","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"TL7ZR5DAN7BE23S5","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"TL7ZR5DA","created_at":"2026-05-18T12:32:53.628368+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/TL7ZR5DAN7BE23S577K5VCK6E6","json":"https://pith.science/pith/TL7ZR5DAN7BE23S577K5VCK6E6.json","graph_json":"https://pith.science/api/pith-number/TL7ZR5DAN7BE23S577K5VCK6E6/graph.json","events_json":"https://pith.science/api/pith-number/TL7ZR5DAN7BE23S577K5VCK6E6/events.json","paper":"https://pith.science/paper/TL7ZR5DA"},"agent_actions":{"view_html":"https://pith.science/pith/TL7ZR5DAN7BE23S577K5VCK6E6","download_json":"https://pith.science/pith/TL7ZR5DAN7BE23S577K5VCK6E6.json","view_paper":"https://pith.science/paper/TL7ZR5DA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.03169&json=true","fetch_graph":"https://pith.science/api/pith-number/TL7ZR5DAN7BE23S577K5VCK6E6/graph.json","fetch_events":"https://pith.science/api/pith-number/TL7ZR5DAN7BE23S577K5VCK6E6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TL7ZR5DAN7BE23S577K5VCK6E6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TL7ZR5DAN7BE23S577K5VCK6E6/action/storage_attestation","attest_author":"https://pith.science/pith/TL7ZR5DAN7BE23S577K5VCK6E6/action/author_attestation","sign_citation":"https://pith.science/pith/TL7ZR5DAN7BE23S577K5VCK6E6/action/citation_signature","submit_replication":"https://pith.science/pith/TL7ZR5DAN7BE23S577K5VCK6E6/action/replication_record"}},"created_at":"2026-05-18T00:08:30.005535+00:00","updated_at":"2026-05-18T00:08:30.005535+00:00"}