{"paper":{"title":"Duality on Banach spaces and a Borel parametrized version of Zippin's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bruno de Mendon\\c{c}a Braga","submitted_at":"2015-08-09T18:27:02Z","abstract_excerpt":"Let SB be the standard coding for separable Banach spaces as subspaces of $C(\\Delta)$. In these notes, we show that if $\\mathbb{B} \\subset \\text{SB}$ is a Borel subset of spaces with separable dual, then the assignment $X \\mapsto X^*$ can be realized by a Borel function $\\mathbb{B}\\to \\text{SB}$. Moreover, this assignment can be done in such a way that the functional evaluation is still well defined (Theorem $1$). Also, we prove a Borel parametrized version of Zippin's theorem, i.e., we prove that there exists $Z \\in \\text{SB}$ and a Borel function that assigns for each $X \\in \\mathbb{B}$ an i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02066","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"}