{"paper":{"title":"Bourgain-Delbaen $\\mathcal{L}^{\\infty}$-sums of Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Despoina Zisimopoulou","submitted_at":"2014-02-26T15:04:07Z","abstract_excerpt":"Motivated by a problem stated by S.A.Argyros and Th. Raikoftsalis, we introduce a new class of Banach spaces. Namely, for a sequence of separable Banach spaces $(X_n,\\|\\cdot\\|_n)_{n\\in\\mathbb{N}}$, we define the Bourgain Delbaen $\\mathcal{L}^{\\infty}$-sum of the sequence $(X_n,\\|\\cdot\\|_n)_{n\\in\\mathbb{N}}$ which is a Banach space $\\mathcal{Z}$ constructed with the Bourgain-Delbaen method. In particular, for every $1\\leq p<\\infty$, taking $X_n=\\ell_p$ for every $n\\in\\mathbb{N}$ the aforementioned space $\\mathcal{Z}_p$ is strictly quasi prime and admits $\\ell_p$ as a complemented subspace. We s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6564","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"}