{"paper":{"title":"On the Bounded Approximation Property in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jes\\'us M.F. Castillo, Yolanda Moreno","submitted_at":"2013-07-16T19:18:42Z","abstract_excerpt":"We prove that the kernel of a quotient operator from an $\\mathcal L_1$-space onto a Banach space $X$ with the Bounded Approximation Property (BAP) has the BAP. This completes earlier results of Lusky --case $\\ell_1$-- and Figiel, Johnson and Pe\\l czy\\'nski --case $X^*$ separable. Given a Banach space $X$, we show that if the kernel of a quotient map from some $\\mathcal L_1$-space onto $X$ has the BAP then every kernel of every quotient map from any $\\mathcal L_1$-space onto $X$ has the BAP. The dual result for $\\mathcal L_\\infty$-spaces also hold: if for some $\\mathcal L_\\infty$-space $E$ some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4383","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"}