{"paper":{"title":"Extending surjective isometries defined on the unit sphere of $\\ell_\\infty(\\Gamma)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio M. Peralta","submitted_at":"2017-09-27T15:38:14Z","abstract_excerpt":"Let $\\Gamma$ be an infinite set equipped with the discrete topology. We prove that the space $\\ell_{\\infty}(\\Gamma),$ of all complex-valued bounded functions on $\\Gamma$, satisfies the Mazur-Ulam property, that is, every surjective isometry from the unit sphere of $\\ell_{\\infty}(\\Gamma)$ onto the unit sphere of an arbitrary complex Banach space $X$ admits a unique extension to a surjective real linear isometry from $\\ell_{\\infty}(\\Gamma)$ to $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09584","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"}