{"paper":{"title":"A forgotten theorem of Pe{\\l}czy\\'nski: $(\\lambda+)$-injective spaces need not be $\\lambda$-injective -- the case $\\lambda\\in (1,2]$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Grzegorz Lewicki, Tomasz Kania","submitted_at":"2022-01-19T19:42:43Z","abstract_excerpt":"Isbell and Semadeni [Trans. Amer. Math. Soc. 107 (1963)] proved that every infinite-dimensional $1$-injective Banach space contains a hyperplane that is $(2+\\varepsilon)$-injective for every $\\varepsilon > 0$, yet is is \\emph{not} $2$-injective and remarked in a footnote that Pe{\\l}czy\\'nski had proved for every $\\lambda > 1$ the existence of a $(\\lambda + \\varepsilon)$-injective space ($\\varepsilon > 0$) that is not $\\lambda$-injective. Unfortunately, no trace of the proof of Pe{\\l}czy\\'nski's result has been preserved. In the present paper, we establish the said theorem for $\\lambda\\in (1,2]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.07837","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.07837/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}