{"paper":{"title":"A universal Banach space with a $K$-unconditional basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Joanna Garbuli\\'nska-W\\k{e}grzyn, Taras Banakh","submitted_at":"2018-01-26T22:09:41Z","abstract_excerpt":"For a constant $K\\geq 1$ let $\\mathfrak{B}_K$ be the class of pairs $(X,(\\mathbf e_n)_{n\\in\\omega})$ consisting of a Banach space $X$ and an unconditional Schauder basis $(\\mathbf e_n)_{n\\in\\omega}$ for $X$, having the unconditional basic constant $K_u\\leq K$. Such pairs are called $K$-based Banach spaces. A based Banach space $X$ is rational if the unit ball of any finite-dimensional subspace spanned by finitely many basic vectors is a polyhedron whose vertices have rational coordinates in the Schauder basis of $X$.\n  Using the technique of Fra\\\"iss\\'e theory, we construct a rational $K$-base"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10064","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":""},"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"}