{"paper":{"title":"1-complemented subspaces of Banach spaces of universal disposition","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":"2017-08-12T21:24:25Z","abstract_excerpt":"We first unify all notions of partial injectivity appearing in the literature ---(universal) separable injectivity, (universal) $\\aleph$-injectivity --- in the notion of $(\\alpha, \\beta)$-injectivity ($(\\alpha, \\beta)_\\lambda$-injectivity if the parameter $\\lambda$ has to be specified). Then, extend the notion of space of universal disposition to space of universal $(\\alpha, \\beta)$-disposition. Finally, we characterize the $1$-complemented subspaces of spaces of universal $(\\alpha, \\beta)$-disposition as precisely the spaces $(\\alpha, \\beta)_1$-injective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03823","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"}