{"paper":{"title":"Metric characterisation of unitaries in JB$^*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Antonio M. Peralta, Mar\\'ia Cueto-Avellaneda","submitted_at":"2019-07-10T14:09:05Z","abstract_excerpt":"Let $M$ be a unital JB$^*$-algebra whose closed unit ball is denoted by $\\mathcal{B}_M$. Let $\\partial_e(\\mathcal{B}_M)$ denote the set of all extreme points of $\\mathcal{B}_M$. We prove that an element $u\\in \\partial_e(\\mathcal{B}_M)$ is a unitary if and only if the set $$\\mathcal{M}_{u} = \\{e\\in \\partial_e(\\mathcal{B}_M) : \\|u\\pm e\\|\\leq \\sqrt{2} \\}$$ contains an isolated point. This is a new geometric characterisation of unitaries in $M$ in terms of the set of extreme points of $\\mathcal{B}_M$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04738","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"}