{"paper":{"title":"Free groups and quasidiagonality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Caleb Eckhardt","submitted_at":"2016-07-07T20:59:46Z","abstract_excerpt":"We use free groups to settle a couple questions about the values of the Pimsner-Popa-Voiculescu modulus of quasidiagonality for a set of operators $\\Omega$, denoted by qd$(\\Omega)$. Along the way we deduce information about the operator space structure of finite dimensional subspaces of $\\mathbb{C}[\\mathbb{F}_d]\\subseteq C^*_{\\ell^p}(\\mathbb{F}_d)$ where $C^*_{\\ell^p}(\\mathbb{F}_d)$ is the so-called $\\ell^p$-completion of $\\mathbb{C}[\\mathbb{F}_d].$ Roughly speaking, we use free groups and qd$(\\Omega)$ to put a quantitative face on the two known qualitative obstructions to quasidiagonality; ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02170","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"}