{"paper":{"title":"Some Banach spaces are almost Hilbert","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Marzett Golden, Tepper L. Gill","submitted_at":"2015-07-27T15:17:27Z","abstract_excerpt":"The purpose of this note is to show that, if $\\mcB$ is a uniformly convex Banach, then the dual space $\\mcB'$ has a \"Hilbert space representation\" (defined in the paper), that makes $\\mcB$ much closer to a Hilbert space then previously suspected. As an application, we prove that, if $\\mcB$ also has a Schauder basis (S-basis), then for each $A \\in \\C[\\mcB]$ (the closed and densely defined linear operators), there exists a closed densely defined linear operator $A^* \\in \\C[\\mcB]$ that has all the expected properties of an adjoint. Thus for example, the bounded linear operators, $L[\\mcB]$, is a $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08611","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"}