{"paper":{"title":"Idempotents of small norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hung Le Pham, Jayden Mudge","submitted_at":"2015-10-13T05:14:04Z","abstract_excerpt":"Let $\\Gamma$ be a locally compact group. We answer two questions left open in [7] and [9]:\n  i) For abelian $\\Gamma$, we prove that if $\\chi_S \\in B(\\Gamma)$ is an idempotent with norm $\\left\\|\\chi_S \\right\\| < \\frac{4}{3}$, then $S$ is the union of two cosets of an open subgroup of $\\Gamma$.\n  ii) For general $\\Gamma$, we prove that if $\\chi_S \\in M_{cb}A(\\Gamma)$ is an idempotent with norm $\\left\\| \\chi_S \\right\\|_{cb} < \\frac{1 + \\sqrt{2}}{2}$, then $S$ is an open coset in $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03535","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"}