{"paper":{"title":"Banach spaces from a construction scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.LO","authors_text":"Fulgencio Lopez","submitted_at":"2016-02-04T01:04:30Z","abstract_excerpt":"We construct a Banach space $\\mathcal X_\\varepsilon$ with an uncountable $\\varepsilon$-biorthogonal system but no uncountable $\\tau$-biorthogonal system for $\\tau<\\varepsilon$. In particular the space have no uncountable biorthogonal system. We also construct a Banach space $\\mathcal X_K$ with an uncountable $K$-basic sequence but no uncountable $K'$-basic sequence, for $1\\leq K'<K$. A common feature of these examples is that they are both constructed by recursive amalgamations using a single construction scheme."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01521","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"}